Unformatted text preview: In order to get the correct answer, you have to set up the integral so that the point of discontinuity is an endpoint. If you didn’t realize that the function is discontinuous at x = 0, you might set up the problem with limits of integration between negative one and one. This would result in a solution with the area under the curve equal to negative two. This answer is incorrect. Notice that the function is squared so it is positive everywhere; the correct answer must also be positive. To set up the integral correctly, use the point of discontinuity, x = 0, as a limit of integration. Because the function 2 1 x is symmetric about the y-axis, find the area under the curve between zero and one and then double the result. Evaluating the antiderivative, − 2 x , as → x results in −∞ . This improper integral diverges....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.
- Spring '10