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Question: \(\int_{0}^{\pi}{e^{\sin^{2}x}\cos^{3}xdx}\)= **OR** For any integer n, \(\int_{0}^{\pi}{e^{\sin^{2...

∫0πesin⁡2xcos⁡3xdx\int_{0}^{\pi}{e^{\sin^{2}x}\cos^{3}xdx}= OR

For any integer n, ∫0πesin⁡2xcos⁡3(2n+1)xdx\int_{0}^{\pi}{e^{\sin^{2}x}\cos^{3}(2n + 1)xdx}=

A

–1

B

0

C

1

D

None of these

Answer

0

Explanation

Solution

Let, f1(x)=cos⁡3x=−f(π−x)f_{1}(x) = \cos^{3}x = - f(\pi - x) and

f2(x)=cos⁡3(2n+1)x=−f(π−x)f_{2}(x) = \cos^{3}(2n + 1)x = - f(\pi - x)

I = 0.