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How to integrate this?

  1. Jan 24, 2015 #1
    1. The problem statement, all variables and given/known data
    How to integrate the double integral cos(x+y) dy dx from 0 to pi and from 0 to pi again.

    2. Relevant equations
    The answer is -4.

    3. The attempt at a solution
    Here's the work:
    u=x+y
    du=dy
    cos(u)du=sin(x+y)
    integral of [sin(x+y)] evaluate from 0 to pi dx from 0 to pi
    integral of (sin(x+pi)-sin(x))dx from 0 to pi
    And what's next?
     
  2. jcsd
  3. Jan 24, 2015 #2

    LCKurtz

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    Integrate again, similar to what you did for the first integral.
     
  4. Jan 24, 2015 #3
    Er...doesn't the final step that you list give you the answer already?
     
  5. Jan 24, 2015 #4
    But I can't. Because sin(x+pi)-sin(x)=sin(x)+sin(pi)-sin(x)=sin(pi)=0. The integral of 0 is?
     
  6. Jan 24, 2015 #5

    LCKurtz

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    ##\sin(a+b)\ne \sin a +\sin b##
     
  7. Jan 24, 2015 #6
    That is most certainly not correct. Can you check your compound angle formula?
     
  8. Jan 24, 2015 #7
    Then what's sin(a+b)?
     
  9. Jan 24, 2015 #8
  10. Jan 24, 2015 #9
    @Fightfish , thank you so much for the info! I got it!
     
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