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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 81 . 3 ...
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 DORAIS
 Math, Calculus

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