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If f is an odd function, then the value of $\int_{- a}^{a} \frac{f (\sin x)}{f (\cos x) + f (\sin^{2} x)} d x$ is equal to

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f(cos⁡x)+f(sin⁡x)

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f(sin⁡x)f(cos⁡x)+fsin2⁡x is odd function since f(sin⁡-x)f(cos⁡-x)+fsin2⁡-x=-f(sin⁡x)f(cos⁡x)+fsin2⁡x since fx is odd∫−aa f(sin⁡x)f(cos⁡x)+fsin2⁡xdx=0

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If f is an odd function, then the value of ∫−aa f(sin⁡x)f(cos⁡x)+fsin2⁡xdx is equal to

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Ready to Test Your Skills?

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If f is an odd function, then the value of $\int_{- a}^{a} \frac{f (\sin x)}{f (\cos x) + f (\sin^{2} x)} d x$ is equal to