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Previous Year Question (PYQs)

If $f:\mathbb R\to\mathbb R$ and $g:\mathbb R\to\mathbb R$ are continuous functions, then evaluate $\displaystyle \int_{-\pi/2}^{\pi/2}[f(x)+f(-x)][g(x)-g(-x)],dx$




Solution

$f(x)+f(-x)$ is an even function $g(x)-g(-x)$ is an odd function Product of even and odd function is odd Integral of odd function over symmetric limits is $0$

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