Solveeit Logo
Login

Question

Question: If n is any integer, then \(\int_{0}^{\pi}{e^{\cos^{2}x}\cos^{3}(2n + 1)xdx}\) is equal to...

If n is any integer, then ∫0πecos⁡2xcos⁡3(2n+1)xdx\int_{0}^{\pi}{e^{\cos^{2}x}\cos^{3}(2n + 1)xdx} is equal to

A

x

B

1

C

0

D

None of these

Answer

0

Explanation

Solution

I=∫0πecos⁡2(π−x).cos⁡3(2n+1)(π−x)dxI = \int_{0}^{\pi}e^{\cos^{2}(\pi - x)}.\cos^{3}(2n + 1)(\pi - x)dx

⇒ I=−∫0πecos⁡2x.cos⁡3(2n+1)xdxI = - \int_{0}^{\pi}{e^{\cos^{2}x}.\cos^{3}(2n + 1)xdx} ⇒ I=−II = - I

⇒ 2I=02I = 0 ⇒ I=0.I = 0.