quiz8soln

quiz8soln - MATH 231 / Spring 2008 Name: Key March 26, 2008...

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Unformatted text preview: MATH 231 / Spring 2008 Name: Key March 26, 2008 1. (3 points) Complete the following theorem from the book: if f is continuous on a polar rectangle R given by 0 a r b, , where 0 - 2, then b f (x, y) dA = R a f (r cos , r sin )r dr d 2. (7 points) Evaluate the integral: 8 0 2 ex dx dy 3 y 4 Although there is a way to integrate this straight away (using the power series for e), we don't really want to do that. Instead, let's flip the integral and see what happens. The region we're integrating over looks as follows: 8 6 4 2 0 0.0 0.5 1.0 1.5 2.0 Now we may determine what happens when we flip the integral: 8 0 2 2 e 3 y x4 x3 0 2 dx dy = 0 ex dy dx = 0 4 x3 ex dx = 4 1 16 (e - 1) 4 1 ...
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