Question

The value of the integration $\underset{-\pi /4}{\overset{\pi /4}{\int }}$$\left(\lambda \left|sinx\right|+\frac{\mu sinx}{1+cosx}+\gamma \right)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

Answer: (B)

$I=2\lambda \underset{0}{\overset{\frac{\pi }{4}}{\int }}sinxdx+\mu \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}tan\frac{x}{2}dx+\gamma \underset{-\frac{\pi }{4}}{\overset{\frac{\pi }{4}}{\int }}dx$
$=2\lambda \left(1-\frac{1}{\sqrt{2}}\right)-0+\gamma \left(\frac{\pi }{2}\right)$($\because tan\frac{x}{2}$ is an odd function)