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Question: Answered & Verified by Expert
$\int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x=$
MathematicsDefinite IntegrationJEE Main
Options:
  • A $\frac{2}{15}$
  • B $\frac{4}{15}$
  • C $\frac{6}{15}$
  • D $\frac{8}{15}$
Solution:
2792 Upvotes Verified Answer
The correct answer is: $\frac{4}{15}$
$\begin{aligned} & \int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x \\ & =\int_{-\pi / 2}^{\pi / 2} \sin ^3 x \cos ^2 x d x+\int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^3 x d x \\ & =0+2 \int_0^{\pi / 2} \sin ^2 x \cos ^3 x d x=0+2 \times \frac{2}{15}=\frac{4}{15}\end{aligned}$

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