0-pi-2-sin-2-xcos-3-xdx-

Question Number 21721 by Isse last updated on 02/Oct/17

\int_{0}^{π / 2} {s i n}^{2} {x c o s}^{3} x d x

Answered by sma3l2996 last updated on 02/Oct/17

= \int_{0}^{π / 2} {s i n}^{2} x (1 - {s i n}^{2} x) c o s x d x = \int_{0}^{π / 2} ({c o s x s i n}^{2} x - {c o s x s i n}^{4} x) d x

= {[\frac{1}{3} {s i n}^{3} x - \frac{1}{5} {s i n}^{5} x]}_{0}^{π / 2} = \frac{1}{3} - \frac{1}{5} = \frac{2}{15}