Question

Solve:

$\stackrel{\pi /2}{\underset{-\pi /2}{\int }}{\sin }^{9}xdx$

• A. $-1$
• B. $1$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

${\int }_{-\pi /2}^{\pi /2}{\sin }^{9}xdx=I$

${\int }_{-\pi /2}^{\pi /2}{\sin }^9(\pi /2-\pi /2-x)dx$

$\Rightarrow {\int }_{-\pi /2}^{\pi /2}{\sin }^9(-x)dx$

$\Rightarrow {\int }_{-\pi /2}^{\pi /2}{\sin }^{9}dx=-I=I$

$\therefore -I=I$

$2I=0$

$\Rightarrow I=0$.