If $f:\mathbb R\to\mathbb R$ and $g:\mathbb R\to\mathbb R$ are continuous functions, then evaluate
$\displaystyle \int_{-\pi/2}^{\pi/2}[f(x)+f(-x)][g(x)-g(-x)],dx$
🎥 Video solution / Text Solution of this question is given below:
$f(x)+f(-x)$ 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 $0$