The z-table has areas expressed as decimals rounded to 4 places, not percents. In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. Normal distribution calculator Enter mean, standard deviation and cutoff points and this calculator will find the area under normal distribution curve. Unfortunately this command does give the value of the shaded area. Calculus Maximus Notes 6. Find the normal curve function: Press 2 nd then VARS : Press 2 (for normalcdf) ** This function has four (4) arguments. A second classic. This area (. z-score calculator - step by step calculation to calculate the normalized value or relative standings of a random or individual sample of the normal distribution with population mean (μ) and standard deviation (σ). To calculate the area enclosed by a curve and the x axis, between two values of x, a and b, we calculate the definite integral of the absolute value of the curve's from a to b. Related Surface Area Calculator | Volume Calculator. Calculate Area Between 2 Curves. Free area under the curve calculator - find functions area under the curve step-by-step. If we add all these typical rectangles, starting from `a` and finishing at `b`, the area is approximately: `sum_{x=a}^\b(y)Deltax` Now if we let `Δx → 0`, we can find the exact area by integration:. The knowledge of the distribution of sediment in a reservoir is necessary for fixing sill elevation of the outlets and the penstock gate elevation to avoid premature loss of services when. Overview of Area Between Two Curves With a few modifications the area under a curve represented by a definite integral can be extended to find the area between to curves. Integral Applications - finds the area of the region bounded by two curves. Related Symbolab blog posts. Note that, since the integral for the parts of the curve below the x-axis are negative, the total area between the points of intersection will be the definite integral of the upper curve minus the definite integral of the lower curve. Example: Find the area in the region bounded by x = 5 x 1 dx 2 5 dy 0 x y2+1dy +2-0-0 x Area nght of the curve: (Shaded Area) 10 Area under the curve: (Shaded Area) x (x 0 dx The area was found by taking vertical partitions. Math 230 Calculus II Brian Veitch Fall 2015 Northern Illinois University Area between Curves In this section we are going to nd the area between curves. 500 to the z-value you just found in step 2. How is the area under the curve calculated for doing in vivo glycemic index estimation? I have performed animal studies for glycemic index (GI) estimation of the developed products. Finding the area between curves expressed as functions of y Video transcript - [Instructor] What we're going to do using our powers of calculus is find the area of this yellow region and if at any point you get inspired, I always encourage you to pause the video and try to work through it on your own. If you have a model, then the algorithm will be straightforward. I have lots of data, so I'd like to do it programmatically. The values you get from the table give you percentages for the area under a curve in decimal form. To know whether you want area on the left, on the right or between two x-values. To help find the height corresponding to the x-value. The method is explained in detail with several tutorials, in which we illustrate the technique with and without a calculator. highest test score achieved and the lowest test score achieved. 40, a calculator gives -0. This video contains plenty of examples and practice problems. Learn term:auc = area under the curve with free interactive flashcards. I have no idea what area should I calculate (because of y=-x-1) Regards. image/svg+xml. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. A second classic. 98(c) Find the area under the standard normal curve to the right of z-2. Use the Wolfram/Alpha Widget: Algebraic-Calculus Area Calculator to enter and check your work. Area under a curve, definite integral, absolute value rules this page updated 19-jul-17 Mathwords: Terms and Formulas from Algebra I to Calculus. highest test score achieved and the lowest test score achieved. Herman's AP Calculus 8,742 views. The TI-84 device, developed by Texas Instruments, is a graphing calculator that can perform scientific calculations as well as graph, compare and analyze single or multiple graphs on a graphing palette. Using your calculator to find area between two curves again - Duration: 3:59. The TI-82 will show you a 1 or 2 for the function number in the upper left hand corner of the screen. Generally we should interpret 192 Chapter 9 Applications of Integration “area” in the usual sense, as a necessarily positive quantity. Area between 3 curves? Will someone help me out and show the steps that should be taken to solve a problem like this? I want a desk top calculator. Free area under the curve calculator - find functions area under the curve step-by-step. How to calculate area under curve? Please Help: In a normal distribution with mean 2. We are also going to assume that. Find the area bounded by y = x2 and y = -2 between x = -1 and x = 1. Best Online Free Calculators - Best online calculator for school and college students to solve easier for math, physics and chemistry equations. 1 Answer to Calculus 2: Chapter 6 Section 6. In today’s video, I go through a problem breakdown from a Calc 1 exam where we’re asked to find the area between two curves. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. The probability P(a>. Area Between Two Curves Calculator. We apply that formula to. Learn term:auc = area under the curve with free interactive flashcards. The area under a curve is the area between the curve and the x-axis. The two curves meet at $\theta=\pi/6$ and $\theta=\pi-\pi/6$. Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step. 7 and the normal random variable x is =8 find Probability Density Function and draw the probability density curve. y=e^4x, y=e^7x, x=1. Easy Steps To Success: A Graphing Calculator Guide For The TI-84 Plus, TI-83, TI-83 Plus, and TI-82 Graphing Calculators gives step-by-step keystrokes and instructions for these calculators, along with examples using these keystrokes to solve problems. Step-by-Step ›. As you can see, one is black and white, and the other has two areas coloured in different colours. ) y = e 3x, 2 x 1 Steps for ﬁnding the Area Between two functions, f(x) and g(x),on[a,b]:. For example, a table value of. The basic technique will be to split our interval up into some number of subintervals of equal length (the number of subintervals is typically given in the problem). Prerequisites. Enter the mean, standard deviation and select whether left tailed or right tailed or two tailed in this normal distribution curve generator to get the result. Question: Find The Area Of The Shaded Region. Solve your calculus problem step by step!. For example, suppose that you want to calculate the shaded area between y = x2 and as shown in this figure. Get the free "Area Between Curves Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. The Area Under a Curve. ∫ dy; where h(y) is the right curve & k(y) is the left curve. Finding the area between two curves in integral calculus is a simple task if you are familiar with the rules of integration (see indefinite integral rules). image/svg+xml. Let's explore the techniques for finding areas between curves in a little more depth. The shaded area on the left graph in the below figure shows the area you want to find. This tests the probability that there is a trend in survival scores across the groups. Area of Surface of Revolution Calculator. 1: Area Between Curves. All of these techniques allows you to answer questions like "what is the probability of obtaining a score between X and Y?". the area between the curve, the x-axis and the two ordinates. Here’s the sliced up area under the calculated curve. Type in any integral to get the solution, steps and graph. 2 Lines Intersection Calculator-- Enter Line 1 Equation-- Enter Line 2 Equation (only if you are not pressing Slope) 2 Lines Intersection Video. formula are not the same a and b we use in the integration step. To know whether you want area on the left, on the right or between two x-values. The calculator will find the tangent line to the explicit, polar, parametric and implicit curve at the given point, with steps shown. Let the circle ( a closed simple curve) have a radius 'a'. You can use the concept of unsigned area to measure the area between curves. Surface area of a cube: A = 6a², where a is the side length. Step-by-Step ›. Practice Makes Perfect. Z - score calculator This calculator can be used to find area under standard normal curve $ ( \mu=0 , \sigma=1 )$. This can be done algebraically or graphically. There is one area. ∫ dy; where h(y) is the right curve & k(y) is the left curve. If you take the value of the area of the first z score and subtract it from the area of the second z score, this difference represents the area under the curve between these 2 z-score values. We want the area that is common to the regions enclosed by the two curves. Learning math takes practice. You can use the concept of unsigned area to measure the area between curves. Most of your integrated signal will be an artifact. Area between curves with multiple boundaries - Duration: 6:54. The three panels below illustrate the process. If we can find a way to represent the height of each of those representative rectangular slices as a positive expression, we can integrate over the interval to find the exact area between the curves. 500 to the z-value you just found in step 2. Area under the normal curve for different values of z: How to use this table: The middle column gives the area under the normal curve that corresponds to the red area in the graph. Steps: Key Sequence: Screens: 1. This reveals which curve is h (right curve) and which is k (left curve). Draw the curves; Find the left intersection point using [2nd][CALC][5:intersect]. Answer to Use a calculator to approximate the area between the following curves:. The knowledge of the distribution of sediment in a reservoir is necessary for fixing sill elevation of the outlets and the penstock gate elevation to avoid premature loss of services when. x=-2 x=2 y=5e^5x y=(4e^5x)+1 I have the answer of 4404. In the tangent line problem, you saw how the limit process could be applied to the slope of a line to find the slope of a general curve. Related Symbolab blog posts. Definite integration finds the accumulation of quantities, which has become a basic tool in calculus and has numerous applications in science and engineering. They cross at (1, 1) — what an amazing coincidence! So you’ve got two separate regions — one from 0 to 1 and another from 1 to 2. (1) Recall finding the area under a curve. The split screen format shows the menus and keystrokes needed to perform or to check. When Δx becomes extremely small, the sum of the areas of the rectangles gets closer and closer to the area under the curve. The area between the curve y = 1/x, the y-axis and the lines y = 1 and y = 2 is rotated about the y-axis. This approximation of the area can be written as:. Regions Between Circles and Squares : A common application of the area of a circle and the area of a square are problems where a circle is circumscribed about a square or inscribed in a square. Calculate the approximate grading scale for a normal grade curve with this Grade Curve Calculator. The fundamental theorem gives us this: given a derivative F'(x) and its antiderivative F(x), the area between the derivative curve F'(x) and an interval [a, b] on the x-axis is equal to the difference in the y values of the antiderivative F(x) at the endpoints of the interval. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Tangent Line Calculator. Students will make comparisons between the estimated area and the actual area. Enter the Function = Lower Limit = Upper Limit = Calculate Area: Need a step by step solution for this problem? >>. Approximate: In order to find the approximate length of the curve, we must approximate each slice by a type of curve whose length we know how to compute. So, first of all we need to graph these curves , we can use table method to graph each of these curves. Free area under between curves calculator - find area between functions step-by-step. Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Here is the sliced up area under the measured curve. Byju's Area under the Curve Calculator is a tool which makes calculations very simple and interesting. The first time most project managers become aware of the existence of S-curves is when they are requested by the client or senior management to include one in their next progress report. Area under the Curve Calculator. If it actually goes to 0, we get the exact area. Find the area under the standard normal distribution curve between z = 0 and z = 2. * Area between curves This is a nifty little program to enhance the computational ability of your TI83 family calculator. The definite integral of `f(x)` from `x = a` to `x = b`, denoted `int_(a)^(b)f(x)\ dx`, is defined to be the signed area between `f(x)` and the `x` axis, from `x = a` and `x = b`. 2—Areas between Curves Area is always positive. 5 and standard deviation = 2. 1: Area Between Curves. 53 into two parts, the first is 1. Enter the Larger Function = Enter the Smaller Function = Lower Bound = Upper Bound = Calculate Area: Computing Get this widget. Next, Prism identifies the peak of each region. The second part of the question requires students to find the area bounded by the curve and the line. Label your answer in correct units. The method is explained in detail with several tutorials, in which we illustrate the technique with and without a calculator. Summary of Contents for Texas Instruments TI-84 PLUS - Graphing Calculator Page 1 TI-84 Plus and TI-84 Plus Silver Edition Guidebook : This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS) Note version 2. The area is computed using the trapezoid rule. Lesson 1: Area Between Curves. Apply integration and area in practical ways with a lesson that follows a curvy road to calculate the area under a curve, or a velocity activity that connects physics, calculus, and robots. We are given the following information: µ = 450, σ = 25 Find the following: P(X > 475) and P(460 < X < 470). (a) Find P(X > 475) Mean =450 X = 475 The formula to compute the Z value appears above. A simple calculator taking expressions as input. Guided Practice 0. You can then divide the area into vertical or horizontal strips and integrate. This area (. We use integration to evaluate the area we are looking for. 05, what is the area under the curve between 1. Area under curve; Area between curves; Volume of solid of revolution; Arc Length; Function Average. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-Nspire and TI-Nspire CAS CHAPTER 11 77 ©2010 Key Curriculum Press Graphing Ranges Use the Data & Statistics application or the Graphs & Geometry application to calculate the probability associated with an area under the normal curve. Author(s) David M. Volume of Solid of Revolution by Integration (Disk method) the Area Enclosed Between 2 Curves. And sometimes we have to divide up the integral if the functions cross over each other in the integration interval. Math 1206 Calculus - Sec. Materials: Graphing calculator. 3 Area between curves. For example, you can use this technique to find the unsigned shaded area in the following figure. I know I need to find the Integral of the equations at some. (There are two ways to solve this problem: we can calculate the area between two functions and using the vertical elements and. Or have software do it for you. To find the area under a curve using Excel, list the x-axis and y-axis values in columns A and B, respectively. Since the two curves cross,. Find the area of the definite integral. For the area applets, we used rectangles to estimate the definite integral $\int_a^bf(t)dt$. Show Instructions. Exercise 1. Finding the volume is much like finding the area, but with an added component of rotating the area around a line of symmetry - usually the x or y axis. Recall that the integral can represent the area between f(x) and the x-axis. com/patrickjmt !! Finding Areas Between Curves. You can then divide the area into vertical or horizontal strips and integrate. The values you get from the table give you percentages for the area under a curve in decimal form. 6 Example 0. Area between curves, you're guaranteed to see at least one of them on the AP test, so you need to be prepared. Find the area bounded by the graphs of the following collection of functions: Solution [Using Flash] Using a TI-85 graphing calculator to find the area between two curves. You may use the provided graph to sketch the curves and shade the enclosed region. Solution: Step 1: To calculate Probability Density Function find `sqrt(2pi)`. The first step is to find the points of intersection of the line of the curve by equating and using the quadratic formula. Free area under between curves calculator - find area between functions step-by-step. How to use the formula to find the area between two curves. However, Chebyshev's Theorem is used for estimating area under the curve of a non bell-shaped distribution. Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step. As you can see, one is black and white, and the other has two areas coloured in different colours. Sometimes you aren't looking for the area under the curve; after all, not every region is between a curve and axis! In this lesson, learn how to find areas between curves as well as areas with. In calculus, the integral of a function allows you to find the area of the region under the function's curve and above the x-axis, as well as the region between two curves. 1a1 Area of a Region Between Two Curves - Calculus - Duration: 7:44. Finish up your unit with an assessment that prompts class members to calculate a data set with normal distribution in two different ways. The split screen format shows the menus and keystrokes needed to perform or to check. This is a perfect study site to get help to do your homework, prepare for a test, or just refresh your memory, etc. The minimum and maximum values of x must be between Xmin and Xmax in the Window editor. We now look at a way to find the area of a region bounded by two or more curves. Area between Curves Calculator. Summary of Contents for Texas Instruments TI-84 PLUS - Graphing Calculator Page 1 TI-84 Plus and TI-84 Plus Silver Edition Guidebook : This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS) Note version 2. Area between curves Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode. Finding the Area with Integration Finding the area of space from the curve of a function to an axis on the Cartesian plane is a fundamental component in calculus. In each case an integral formula is given. The area that your calculator will actually evaluate is the area of the rectangles shown in Figure 2 (below). To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration. Area between 3 curves? Will someone help me out and show the steps that should be taken to solve a problem like this? I want a desk top calculator. ** Example 1: Let mean = 64. You can approximate the area under a curve by using left sums. So let's say we care about the region from x equals a to x equals b between y equals f of x and y is equal to g of x. Graph the curves and draw a representative rectangle. All of these techniques allows you to answer questions like "what is the probability of obtaining a score between X and Y?". Finding the area between curves expressed as functions of y Video transcript - [Instructor] What we're going to do using our powers of calculus is find the area of this yellow region and if at any point you get inspired, I always encourage you to pause the video and try to work through it on your own. If your curves are not in y 1 or y 2, then you can use the up or down arrow keys to select the different curves. Materials: Graphing calculator. For example, say you want the exact area under a curve between two points, 0 and 3. In this section we will explore how to find the area between two curves. Area under the Curve Calculator. Here is a list of topics: 1. In the bell curve, the highest point is the one that has the highest probability of occurring, and the probability of occurrences goes down on either side of the curve. Michael Borcherds. Label your answer in correct units. Finding the area between curves expressed as functions of y Video transcript - [Instructor] What we're going to do using our powers of calculus is find the area of this yellow region and if at any point you get inspired, I always encourage you to pause the video and try to work through it on your own. 2: Areas between Curves Page 1 of 6 §6. 5 ** To type in E use 2 nd then comma. In general, you can skip parentheses, but be very careful: e^3x is `e^3x`, and e^(3x) is `e^(3x)`. The area under the curve can be approximated by breaking the x-interval between and into intervals of equal width, and computing the sum of rectangles, which intersect with the function as displayed on the figure below. To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration. 1: Area Between Curves. Its area is `yΔx`. Explanation is given as to what equations should be integrated in order to find the required area. They are: lower bound, upper bound, mean, standard deviation. Math 230 Calculus II Brian Veitch Fall 2015 Northern Illinois University Area between Curves In this section we are going to nd the area between curves. Z - score calculator This calculator can be used to find area under standard normal curve $ ( \mu=0 , \sigma=1 )$. Practice Makes Perfect. Find more Mathematics widgets in Wolfram|Alpha. You'll be finding intersections, setting up integrals. You will also learn the equation for sector area. Byju's Area under the Curve Calculator is a tool which makes calculations very simple and interesting. Target AUC typically ranges between 5 and 7. If it actually goes to 0, we get the exact area. Step by step solutions to two problems. For the Second Curve, hit enter. 2 between x = 3 and x = 5 using 8 rectangles to do the approximation. For each problem, find the area under the curve over the given interval. Both types of integrals are tied together by the fundamental theorem of calculus. Solution: Step 1: To calculate Probability Density Function find `sqrt(2pi)`. This free online calculator will help you to find the area of a triangle using the Heron's formula. The area that your calculator will actually evaluate is the area of the rectangles shown in Figure 2 (below). (You can do this on the calculator. We now look at a way to find the area of a region bounded by two or more curves. 4, we can use the normal curve to approximate areas (probabilities) between different values of Y that follow a normal distribution Y ~ N P,V What we have to do is standardize Y. Here is a set of practice problems to accompany the Area Between Curves section of the Applications of Integrals chapter of the notes for Paul Dawkins Calculus I course at Lamar University. The area under a curve is the area between the curve and the x-axis. Area between Two Curves Calculator. Steps to find the area between two curves 1. Add up the areas of the two regions to get the total area. Introduction. Figure the area of the region on the right. This calculates the area between two curves, Y1 and Y2. Free linear first order differential equations calculator - solve ordinary linear first order differential equations step-by-step. Area and definite integrals. If more than two survival curves are compared, and there is a natural ordering of the groups, then MedCalc can also perform the logrank test for trend. Free linear first order differential equations calculator - solve ordinary linear first order differential equations step-by-step. Answer to Use a calculator to approximate the area between the following curves:. area between curves. This video contains plenty of examples and practice problems. 4, we can use the normal curve to approximate areas (probabilities) between different values of Y that follow a normal distribution Y ~ N P,V What we have to do is standardize Y. The area between the x-axis and the graph of x = x(t), y = y(t) and the x-axis is given by the definite integral below. To find the area under a curve using Excel, list the x-axis and y-axis values in columns A and B, respectively. This calculus video tutorial explains how to find the area between two curves with respect to x and y. Area Under a Curve from First Principles. 34(d) Find the area under the. The two curves meet at $\theta=\pi/6$ and $\theta=\pi-\pi/6$. Calculate Area Between 2 Curves. It also helps find the limits of integration if you do not already know them. Also (frankly), 1/3 seconds of sampling seems quite rare for a step-like response, if you want to integrate the difference. On-screen applet instructions: The applet depicts the total area between two curves, as well as the net area. And any area below the x-axis is considered negative. Be sure to make a diagram showing one typical Riemann rectangle; Show the integral you will calculate. For the area applets, we used rectangles to estimate the definite integral $\int_a^bf(t)dt$. In the bell curve, the highest point is the one that has the highest probability of occurring, and the probability of occurrences goes down on either side of the curve. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-Nspire and TI-Nspire CAS CHAPTER 11 77 ©2010 Key Curriculum Press Graphing Ranges Use the Data & Statistics application or the Graphs & Geometry application to calculate the probability associated with an area under the normal curve. An area between two curves can be calculated by integrating the difference of two curve expressions. Normal Distribution. Formula to calculate average value of a function is given by: Enter the average value of f(x), value of interval a and b in the below online average value of a function calculator and then click calculate button to find the output with steps. area between curves. Enter the Function = Lower Limit = Upper Limit = Calculate Area: Need a step by step solution for this problem? >>. 4: AVERAGE VALUE AND AREA BETWEEN CURVES 3 Example 3. Draw a picture and shade the desired region. Math 230 Calculus II Brian Veitch Fall 2015 Northern Illinois University Area between Curves In this section we are going to nd the area between curves. 51 Step 2:. Steps to Find the Area Between Two Curves 1. Step 3 : Let us use integral calculus to find the area of the circle. We apply that formula to. Recall that the integral can represent the area between f(x) and the x-axis. 1: Area between Two Curves (page 333) Section 6. Be sure to rst accurately graph this region on the axes below. The third area is between z-scores of -2. ) y = e 3x, 2 x 1 Steps for nding the Area Between two functions, f(x) and g(x), on [a;b]:. An online calculator to find and graph the intersection of two lines. To help find the height corresponding to the x-value. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find triangle area using the Heron's formula. The best way is always to draw a sketch of the curve over the required range of values of x. Areas under the x-axis will come out negative and areas above the x-axis will be positive. Get the free "Calculate the Area of a Polar curve" widget for your website, blog, Wordpress, Blogger, or iGoogle. Since the two curves cross,. Here’s the sliced up area under the calculated curve. You can then divide the area into vertical or horizontal strips and integrate. Find the area of the definite integral. Write the integral that represents the area bounded by the functions and. How to find the area between 2 curves using integration, and how the formula is obtained from first principles. Although you can find the area of a curve by manually solving an equation, the TI-84 calculator can find the area. Area between Curves Calculator. Summary of Contents for Texas Instruments TI-84 PLUS - Graphing Calculator Page 1 TI-84 Plus and TI-84 Plus Silver Edition Guidebook : This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS) Note version 2. The area under a curve between two points can be found by doing a definite integral between the two points. Target AUC typically ranges between 5 and 7. There is one area. In Prism, a curve (created by nonlinear regression) is simply a series of connected XY points, with equally spaced X values. Here we are not given a specific interval, so it must be the case that there is a "natural'' region involved. The modern way is to use a computer (like the online calculator below) to do the computation for you. Target AUC typically ranges between 5 and 7. Learn term:auc = area under the curve with free interactive flashcards. 1: Area Between Curves. I think that you will find the concept very easy, since we already know how to find the area between a curve and the x-axis. However, Chebyshev’s Theorem is used for estimating area under the curve of a non bell-shaped distribution. 3 Areas under a Normal Curve Like the density curve in Section 3. 5 , and the second is. The area of the region between the curves is defined as the integral of the upper curve minus the integral of the lower curve over each region. We should never just assume that because limits on \(x\) were given in the problem statement that the curves will not intersect anywhere between the given limits. How to find the area between two curves that are functions of y. Using your calculator to find area between two curves again - Duration: 3:59. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Related Surface Area Calculator | Volume Calculator. * Area between curves This is a nifty little program to enhance the computational ability of your TI83 family calculator. The regions are determined by the intersection points of the curves. Find the area bounded by x = y2 -1, x = -2, y = -1, and y = 1.