Mathematics

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


ANSWER

$$2$$


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
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