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

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

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

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

, is

View answer and explanation

Correct option: A

Option A is correct because the integrand is an odd function, and the integral of an odd function over a symmetric interval is zero.

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