Mathematics

# The value of $\displaystyle \int_{-\pi /2}^{\pi /2}\sqrt{\frac{1}{2}\left ( 1-\cos 2x \right )}$ dx is

$2$

##### SOLUTION
$\displaystyle I=\int_{-\pi /2}^{\pi /2}\sqrt{\frac{1}{2}.2\sin ^{2}x}dx=\int_{-\pi /2}^{\pi /2}\left | \sin x \right |dx,$
$\displaystyle =2\int_{0}^{-\pi /2}\left | \sin x \right |dx$
$\displaystyle =2\int_{0}^{-\pi /2}\sin x dx,$   $\displaystyle \because \left | \sin x \right |=\sin x$ on the interval $\displaystyle \left ( 0, \pi /2 \right )$
$\displaystyle =2\left ( -\cos x \right )^{\pi /2}_{0}=2$

Ans: B

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 126

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