$\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \,\,{\sin ^4}\,\,x\,\,{\cos ^6}\,\,x\,\,dx$ is equal to

$\frac{{3\,{\rm{\pi }}}}{{256}}$

$\frac{{3\,{\rm{\pi }}}}{{64}}$

$\frac{{3\,{\rm{\pi }}}}{{572}}$

$\frac{{3\,{\rm{\pi }}}}{{128}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_{ - \pi /2}^{\pi /2} \,\,{\sin ^4}\,\,x\,\,{\cos ^6}\,\,x\,\,dx

is equal to

View answer and explanation

Correct option: C

\frac{{3\,\mathrm{\pi }}}{{256}}

Option C (

\frac{{3\\,\mathrm{\pi }}}{{256}}

) is correct because the integral of the even function is solved using the Gamma function.

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