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How to solve this triple integral?

  1. Nov 12, 2008 #1
    \int \int \int cos(u + v + w)dudvdw (all integrals go from 0 to pi).

    I've tried using u substitution for each integral but I end up with a huge integral.
     
    Last edited: Nov 12, 2008
  2. jcsd
  3. Nov 12, 2008 #2

    HallsofIvy

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    I don't see why. To integrate cos(u+v+w)du, let x= u+ v+ w so dx= du. The integral becomes [itex]\int[/itex] cos(x)dx= -sin(x)+ C= -sin(u+ v+ w)+ C. Evaluating that at 0 and pi gives -sin(pi+ v+ w)+ sin(v+ w). But sin(x+ pi)= -sin(x) so that is just 2 sin(v+w).

    Now integrate 2sin(v+w) dv by letting x= v+ w so dx=dv.
     
  4. Nov 12, 2008 #3
    I don't understand sin(x+ pi)= -sin(x). Is that an identity I am forgetting about?
     
  5. Nov 12, 2008 #4

    HallsofIvy

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    Do you know what the graph of y= sin(x) looks like?
     
  6. Nov 12, 2008 #5
    Oh, I see. It's a shift, correct?
     
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