Integral Calculus

JEE Main level, single correct, medium

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The value of the definite integral ∫−π/2π/2sin⁡3xcos⁡2x dx\int_{-\pi/2}^{\pi/2} \sin^3 x \cos^2 x \, dx is:

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Answer: (D) 00

The integrand f(x)=sin⁡3xcos⁡2xf(x) = \sin^3 x \cos^2 x is an odd function because f(−x)=−f(x)f(-x) = -f(x). The integral over symmetric limits is 0.

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