$\mathop \smallint \limits_{ - \pi /2}^{\pi /2} {\sin ^2}\,\,x\,\,{\cos ^2}\,\,x\,\,\left( {\sin \,\,x\,\, + \,\,\cos \,\,x} \right)\,\,dx = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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

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Correct option: B

4/15

Option B (

4/15

) is correct. The integral is evaluated by splitting it into odd and even functions and using trigonometric identities.

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