quiz_07B - Z 1 xye x 2 y dx = Z y e u du [ u = x 2 y, du =...

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Math 213 — Quiz 7 Name Solution 1. Calculate the double integral RR R xye x 2 y dA where R = [0 , 1] × [0 , 2]. This is an instance where the choice of order of integration makes a big difference. The easiest order is ZZ R xye x 2 y dA = Z 2 0 Z 1 0 xye x 2 y dxdy. (The other order requires integration by parts.) For the inside integral,
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Unformatted text preview: Z 1 xye x 2 y dx = Z y e u du [ u = x 2 y, du = 2 xy dx ] = [ e u ] y u =0 = e y-1 . For the outside integral, Z 2 ( e y-1) dy = [ e y-y ] 2 y =0 = ( e 2-2)-( e-0) = e 2-3 . Therefore, RR R xye x 2 y dA = e 2-3....
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