Question

The value of the integration $\underset{-\pi /4}{\overset{\pi /4}{\int }}(\lambda |\sin x|+\frac{\mu \sin x}{1+\cos x}+\gamma )dx$

• A. is independent of $\lambda$ only
• B. is independent of $\mu$ only
• C. is independent of $\gamma$ only
• D. depends on $\lambda$, $\mu$ and $\gamma$

Answer 1

The correct option is B is independent of $\mu$ only

$I=\underset{-\pi /4}{\overset{\pi /4}{\int }}(\lambda |\sin x|+\frac{\mu \sin x}{1+\cos x}+\gamma )dx$
$=2\lambda \underset{0}{\overset{\frac{\pi }{4}}{\int }}\sin xdx+0+\frac{\gamma \pi }{2}$
$=2\lambda (1-\frac{1}{\sqrt{2}})+\frac{\gamma \pi }{2}$
which is independent of $\mu$