Mathematics

# The value of the integration $\displaystyle\int^{\pi/4}_{-\pi/4}\left(\lambda |\sin x|+\dfrac{\mu \sin x}{1+\cos x}+\gamma\right)dx$.

Is independent of $\mu$ only

##### SOLUTION
$I=2\lambda\displaystyle\int^{\dfrac{\pi}{4}}_0\sin x dx+\mu\displaystyle\int^{\dfrac{\pi}{4}}_{-\dfrac{\pi}{4}}\tan \dfrac{x}{2}dx+\gamma\displaystyle\int^{\dfrac{\pi}{4}}_{-\dfrac{\pi}{4}}dx$
$=2\lambda\left(1-\dfrac{1}{\sqrt{2}}\right)-0+\gamma\left(\dfrac{\pi}{2}\right)$
$(\because \tan\dfrac{x}{2}$ is an odd function$)$.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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