# Evaluate: ∫ √ 1 − Cos 2 X 2 D X - Mathematics

Sum

Evaluate:

$\int\sqrt{\frac{1 - \cos 2x}{2}}dx$

#### Solution

$\int\sqrt{\frac{1 - \cos 2x}{2}}dx$
=∫ \sqrt {{2 sin_2 x }/{2}} dx   [∴ 1 - cos 2x = 2 sin ^2 x]
$= \int\text{sin x dx}$
$= - \cos x + C$

Concept: Evaluation of Definite Integrals by Substitution
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.1 | Q 2.2 | Page 4