Tricky Integral !

Calculus Level 2

if f(x) and g(x) are 2 real valued functions such that : $f:R \rightarrow R$ $g:R \rightarrow R$

then the value of the integral : $\int_{-\pi/2}^{\pi/2}[(f(x) + f(-x)][g(x) - g(-x)] dx = ?$

\pi

-1

0

\pi/2

1 solution

Aporajita Tume
Oct 13, 2014

as here is no specific function we consider the f(-x)=-f(x). and so there is nothing to integrate. so the ans is 0