quiz_08C - Math 213 Quiz 8 Name Solution 1/2 1 Evaluate the...

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Unformatted text preview: Math 213 -- Quiz 8 Name Solution 1 /2 1. Evaluate the integral 0 arcsin(y) cos(x) 1 + cos2 (x) dx dy by changing the order of in- tegration. Changing the order of integration, we obtain 1 /2 I= 0 cos(x) 1 + cos2 (x) dx dy arcsin(y) /2 sin(x) = 0 /2 0 cos(x) 1 + cos2 (x) dy dx = 0 sin(x) cos(x) 1 + cos2 (x) dx. Substituting u = cos(x), du = - sin(x) dx, we have 0 I=- 1 u 1 + u2 du = 0 1 u 1 + u2 du Subsitituting v = 1 + u2 , dv = 2u du, we find 1 I= 2 2 1 1 v dv = (23/2 - 13/2 ) = 3 8-1 . 3 ...
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