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Homework Help: Double integral polar cordiantes

  1. Nov 16, 2012 #1
    Hi, I need help with this problem

    Evaluate the given integral by changing to polar cordinates

    ∫∫xydA where D is the disc with centre the origin and radius.

    My solution so far.

    I believe this would give a circle with radius 3 in xy plane. And then x=r*cos(θ) and y=r*sin(θ)

    So ∫(∫((r*cos(θ)*r*sin(θ))*r,r,0,3),θ,0,2∏)

    But the result is suppose to be zero.
    What am I doing wrong?
  2. jcsd
  3. Nov 16, 2012 #2
    Ohh never mind, the result is correct :P
    Just me who needs to learn how to use my calculator.

    I guess it did not make seance that a circle with radius 3 would give 0 as a result, but perhaps it's because z=x*y --> z=0 <> 0=x*y so x=0/y --> x=0 and y=0/x --y=0
    Is that a correct interpretation?
  4. Nov 16, 2012 #3


    Staff: Mentor

    And radius what?
    That's what I get.

    Why do you think that z = 0?
    Edit: Added the inner integral.
    The integral looks like this:
    $$ \int_{\theta = 0}^{2\pi}\int_{r=0}^3 rcos(\theta) \cdot rsin(\theta) r~dr~d\theta$$

    If you carry out the integration, you get a value of 0.
    Last edited: Nov 16, 2012
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