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Ifint0^(npi)f(cos^2x)dx=kint0^pif(c0s^2x...

`Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(c0s^2x)dx ,t h e nfin dt h ev a l u ekdot`

Text Solution

Verified by Experts

The correct Answer is:
`n`
Since `cos^(2)x` is a periodic function with period `pi` so is `f(cos^(2)x)`.
Hence `int_(0)^(pi) f(cos^(2)x)dx=n int_(0)^(pi) f(cos^(2)x)dx` or `k=n`
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