RedAssign6[1].1 - Imagine calculating the area of the...

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Unit: Improper Integrals Module: Convergence and Divergence of Improper Integrals The First Type of Improper Integral www.thinkwell.com info@thinkwell.com Copyright 2001, Thinkwell Corp. All Rights Reserved. 1458 –rev 06/14/2001 An improper integral is a definite integral with one of the following properties: the integration takes place over an infinite interval or the integrand is undefined at a point within the interval of integration. With some improper integrals, the area of the region under the curve is finite even though the region extends to infinity. An improper integral that is infinite diverges. An improper integral that equals a numerical value converges. A definite integral is considered an improper integral if it has one of these properties: the integration is over an infinite interval, or its integrand is undefined at a point within the interval of integration.
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Unformatted text preview: Imagine calculating the area of the region under the curve = 2 1 y x starting at x = 1 and moving to the right. You would integrate the function from 1 to and solve the improper integral. The solution of the integral is one. This means that the area under the curve to the right of x = 1 has an area of one. You can think about this area repackaged into the square bounded by the origin and the point (1,1). Because this improper integral has a finite value, it converges. An improper integral diverges if its value is infinite. Imagine calculating the area under the curve = 1 starting at x = 1 and moving to the right. You would integrate the function from 1 to and solve the improper integral. In this example, the value of the integral is infinity, meaning that the area under the curve is infinitely large. 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.

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