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$C[-\pi, \pi], f(x)=x$ and $g(x)= \cos 2x$ I am having a difficulties integrating this function. I dont know where I am messing up. Please help me :D

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and I don't know, what you mean? Maybe $\int_{-\pi}^\pi x\cos 2x dx$? This is $0$, do you know why$ – draks ... Feb 27 '12 at 15:40
well idk latex but I will show u the formula – Sarah Feb 27 '12 at 15:59
(<f,g>)/(<g,g>)g – Sarah Feb 27 '12 at 16:00
so <f,g> is what u have showed but i don't get know how to integrate that function – Sarah Feb 27 '12 at 16:01
ohh i see. ya I get it now soit orthogonal already ok thanks @draks – Sarah Feb 27 '12 at 16:06
up vote 1 down vote accepted

Here are three approaches for calculating $\int_{-\pi}^\pi x\cos 2x$. These are only hints, as this is a homework problem:

  1. Use integration by parts, by defining $f(x)=x,\ g(x)=\cos 2x$.
  2. Use the fact that the integrand is an odd function of $x$. What is the integral of an odd function on a segment that is symmetric around $0$?
  3. Ask Wolfram Alpha and click "show steps".
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Thanks @yohBS That was helpful – Sarah Feb 27 '12 at 16:24

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