$\smallint \sqrt {1\,\, + \,\,\cos \,\,x} \,dx$ is equal to

$2\,\,\sqrt 2 \,\,\cos \,\,\frac{x}{2}\,\, + \,\,c$

$\sqrt 2 \,\,\cos \,\,\frac{x}{2}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \sqrt {1\,\, + \,\,\cos \,\,x} \,dx

is equal to

View answer and explanation

Correct option: B

2\,\,\sqrt 2 \,\,\sin \,\,\frac{x}{2}\,\, + \,\,c

Option B,

2\,\,\sqrt 2 \,\,\sin \,\,\frac{x}{2}\,\, + \,\,c

, is correct because using trigonometric identities, the integral can be simplified and solved, resulting in this expression.