If $\mathop \smallint \nolimits_0^{\pi /2} \,\,{\sin ^6}\,\,x\,dx = \frac{{5\,\pi }}{{32}}$, then the value of $\mathop \smallint \nolimits_{ - \pi }^\pi \,\,({\sin ^6}x\,\, + \,\,{\cos ^6}\,\,x)\;\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_0^{\pi /2} \,\,{\sin ^6}\,\,x\,dx = \frac{{5\,\pi }}{{32}}

, then the value of

\int \nolimits_{ - \pi }^\pi \,\,({\sin ^6}x\,\, + \,\,{\cos ^6}\,\,x)\;\,\,dx

View answer and explanation

Correct option: D

5\,\mathrm{\pi }\,\,/\,\,4

Option D (

5\,\mathrm{\pi}\,/\,4

) is correct because the integral can be simplified using trigonometric identities and the given value of the integral from 0 to

\pi/2

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