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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.
- Spring '10