Question Number 64328 by Chi Mes Try last updated on 16/Jul/19
![Let f : R→R, g : R→R be continuous functions. Then ∫_(−π/2) ^(π/2) [ f(x)+f(−x) ] [ g(x)(g(−x) ] dx =](Q64328.png)
$$\mathrm{Let}\:\:{f}\::\:{R}\rightarrow{R},\:{g}\::\:{R}\rightarrow{R}\:\:\mathrm{be}\:\mathrm{continuous} \\ $$$$\mathrm{functions}.\:\mathrm{Then} \\ $$$$\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\:\left[\:{f}\left({x}\right)+{f}\left(−{x}\right)\:\right]\:\left[\:{g}\left({x}\right)\left({g}\left(−{x}\right)\:\right]\:{dx}\:=\right. \\ $$