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Question: If f is an odd function, then I = \(\int_{- a}^{a}\frac{f(sinx)}{f(cosx) + f(sin^{2}x)}\)dx...

If f is an odd function, then I = ∫−aaf(sinx)f(cosx)+f(sin2x)\int_{- a}^{a}\frac{f(sinx)}{f(cosx) + f(sin^{2}x)}dx

A

Can’t be evaluated

B

I = 0

C

I = π2\frac{\pi}{2}

D

None of these

Answer

I = 0

Explanation

Solution

Since the denominator is even and the numerator f(sin (–x)) = f (–sinx)= –f (sin x) is odd, (as f is odd function), the integral is equal to zero