First slide

Evaluation of definite integrals

Question

$\int_{0}^{π} \sqrt{\frac{\cos 2 x + 1}{2}} dx$ is equal to

Moderate

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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