First slide

Evaluation of definite integrals

Question

The value of the integral $\int_{0}^{100 π} \sqrt{1 - \cos 2 x} d x$ is

Moderate

A

$100 \sqrt{2}$
B

$200 \sqrt{2}$
C

$0$
D

$100 π$

Solution

We have $\sqrt{1 - \cos 2 x} = \sqrt{2} | \sin x | .$ Since the period of $| \sin x |$ is $π,$
so $\int_{0}^{100 π} \sqrt{1 - \cos 2 x} d x =$ $\sqrt{2} \int_{0}^{100 π} | \sin x | d x = 100 \sqrt{2} \int_{0}^{π} \sin x d x = 200 \sqrt{2} .$

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