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For any integer n, the integral int0^pie...

For any integer `n`, the integral `int_0^pie^(cos^x)cos^3(2n+1)xdx` has the value

A

`pi`

B

1

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` f(x) = e^(cos^(2)x).cos^(3) (2n+1)x`
Then, ` f(pi-x) = e^(cos^(2)(pi-x)).cos^(3) [ (2n-1)pi-(2n+1)x]`
` = -e^(cos^(2)x).cos^(3)(2n+1)x`
` rArr f(pi-x) = - f(x)`
` :. int_(0)^(pi) e^(cos^(2)x).cos^(3) (2n+1)x dx = 0 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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