Exam 2 Solutions 2011

Dont forget the limits 4 10 points find 0 solution

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Unformatted text preview: 2 sin4 (t) cos3 (t) dt. (Don’t forget the limits!) 4. (10 points) Find 0 Solution: (corrected) cos3 (t) = (1 − sin2 (t)) cos(t) so π /2 π /2 sin4 (t) cos3 (t) dt = 0 0 sin4 (t)(1 − sin2 (t)) cos(t) dt Substitute u = sin(t), du = cos(t)dt. The limits change: if x = 0 then u = sin(0) = 0; if x = π/2 then u = sin(π/2) = 1, so π /2 0 1 sin4 (t)(1 − sin2 (t)) cos(t) dt = u4 (1 − u2 )du 0 1 = 0 u4 − u6 du 1 u7 u5 − = 5 70 2 11 =−= 57 35 5. (10 points) Find tan2 (θ)dθ. Page 2 Solution: (correc...
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This document was uploaded on 03/05/2014 for the course MAT 193 at CSU Dominguez Hills.

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