The value of $\mathop \smallint \nolimits_{ - \pi }^\pi \,\,\left( {1 - {x^2}} \right)\sin \,\,x\,\,{\cos ^2}\,\,x\;\,dx\;$ is

$\pi \,\, - \,\,\frac{{{\pi ^3}}}{3}$

$\frac{7}{2}\,\, - \,\,2{\pi ^3}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Understanding +4 | -1

The value of

\int \nolimits_{ - \pi }^\pi \,\,\left( {1 - {x^2}} \right)\sin \,\,x\,\,{\cos ^2}\,\,x\;\,dx\;

View answer and explanation

Correct option: A

\mathrm{0}

Option A (0) is correct because the integrand is an odd function, and the integral of an odd function over a symmetric interval from

-\pi

\pi

is zero.

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