∫0π cos⁡2x+12dx is equal to

A
0
B
2
C
-2
D
None of these

Solution:

$\begin{aligned} \int_{0}^{π} \sqrt{\frac{\cos 2 x + 1}{2}} dx = \int_{0}^{π} \sqrt{\cos^{2}} xdx = \int_{0}^{π} | \cos x | dx \\ = \int_{0}^{π / 2} \cos xdx - \int_{π / 2}^{π} \cos xdx = 2 \end{aligned}$

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