$\smallint \sqrt {1 + \sin \,\,\frac{x}{4}} \,dx$ is equal to

$\frac{1}{8}\,\,\left( {\sin \,\,\frac{x}{8}\,\, - \,\,\cos \,\,\frac{x}{8}} \right) + c$

$8\,\,\left( {\cos \,\,\frac{x}{8}\,\, - \,\,\sin \,\,\frac{x}{8}} \right) + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \sqrt {1 + \sin \,\,\frac{x}{4}} \,dx

is equal to

View answer and explanation

Correct option: A

8\,\,\left( {\sin \,\,\frac{x}{8}\,\, - \,\,\cos \,\,\frac{x}{8}} \right) + c

Option A (

8\,\,\left( {\sin \,\,\frac{x}{8}\,\, - \,\,\cos \,\,\frac{x}{8}} \right) + c

) is correct because it is the result of simplifying the integrand using trigonometric identities and integrating.