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Question

The value of the integral $$\displaystyle \int_{0}^{\pi}\sqrt{\frac{1+\cos 2x}{2}} dx$$ is


A
-2
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B
2
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C
0
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D
-3
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Solution

The correct option is B 2
$$\int_{0}^{\pi}\sqrt{\dfrac{1+cos2x}{2}}dx=\int_{0}^{\pi}\left | cosx \right |dx$$
$$\int_{0}^{\pi/2} cosx\ dx-\int_{\pi/2}^{\pi} cos xdx$$
$$sinx\ \int_{0}^{\pi/2}-sinx\int_{\pi/2}^{\pi}$$
$$=1-(-1)$$
$$=2$$
Hence, option 'B' is correct.

Mathematics

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