Show that the given functions are orthogonal on the indicated interval.

Question

F1(x)=x , F2(x)=cos2x  ,[-pi/2,pi/2]

Answer 1

if you are using the inner product <f(x),g(x)> = ∫f(x) dx from -π/2 to π/2, you just need to evaluate the integral:

∫x cos (2x) dx from -π/2 to π/2 which is equal to 0 (using intgration by parts), so, infact, the functions are orthogonal.