Question

The value of $\underset{-\pi /4}{\overset{\pi /4}{\int }}{\sin }^{103}x.{\cos }^{101}xdx$ is

• A. $(\frac{\pi }{4}{)}^{103}$
• B. $(\frac{\pi }{4}{)}^{101}$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

$f\left(x\right)={\sin }^{103}x.{\cos }^{101x}$
$f(-x)=-{\sin }^{103}x.{\cos }^{101}x$
$f\left(x\right)$ is odd function.
Therefore, $\underset{-\pi /4}{\overset{\pi /4}{\int }}{\sin }^{103}x.{\cos }^{101}xdx=0$