Practice Problems: Trigonometric Integrals

2 cos2 x = 1 + cos2x 2 1. (a) We have even powers of both sine and cosine, so we convert each using the half-angle formula to reduce the powers by half, and simplify the resulting integrand: Z sin4 xcos4 xdx = Z 1 cos2x 2 2 1 + cos2x 2 2 dx = Z 1 2cos2x+ cos2 2x 4 1 + 2cos2x+ cos2 2x 4 dx = 1 16 Z ................
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