The value of $\int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx$ is……….

We have, $f(x) = \int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx$

$f( - x) = \int_{ - \pi }^\pi {{{\sin }^3}} ( - 2) - {\cos ^2}( - x)dx$

$= - f(x)$

Since, $f(x)$ is an odd function.
therefore,$\int_{ - \pi }^\pi {{{\sin }^3}} x{\cos ^2}xdx = 0$