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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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    Yes, you are correct. Sorry about that.@3Sphere2012-02-27

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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 helpful2012-02-27