Question

Solve
${\int }_{-\pi /4}^{\pi /4}{x}^5{\cos }^{2}xdx$

Answer 1

We have,

$I={\int }_{-\pi /4}^{\pi /4}{x}^5{\cos }^{2}xdx$

Here, the function is odd.

Therefore

$I=-{\int }_{-\pi /4}^{\pi /4}{x}^5{\cos }^{2}xdx$

Therefore,

$2I=0$

$I=0$

Hence, this is the answer.