Question

Find the Orthogonal Projection of
f onto g. Use the inner product in C[a,b]

C[-pi, pi] f(x)=x and g(x)= cos 2x

Answer 1

if i remember correctly this is
\[\int_{-\pi}^{\pi}x\cos(2x)dx\]

Answer 2

yes that is correct but i am having difficulties integrating

Answer 3

oh parts for this one. pretty sure it is zero

Answer 4

oh wait it is zero from your eyeballs because
\[h(x)=x\cos(x)\] is odd and you are integrating from
\[-\pi\] to \[\pi\]

Answer 5

This is the formula