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Double integral, polar coordinates

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate [tex]\int[/tex][tex]\int[/tex]T (x^2+y^2) dA, where T is the triangle with the vertices (0,0)(1,0)(1,1)

    2. Relevant equations

    3. The attempt at a solution

    [tex]\int[/tex] d[tex]\theta[/tex] [tex]\int[/tex] r^3 dr

    Thats how far I got, not really sure about boundries on r. First integrals boundrie should be 0 to pi/4. Is polar coordinates a good idea? Should I try some other change of variabel?

    Help is appreciated

  2. jcsd
  3. Feb 16, 2010 #2


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    Polar coordinates can be made to work but they are not the natural way to work this problem. There are no circles involved in the region. Just set it up as a normal dydx integral.
  4. Feb 16, 2010 #3
    I wouldn't do this in polar, though the x^2+y^2 makes it tempting...

    Draw out the triangle and figure out the equations for the lines that make it up, use these lines as your bounds for your double integral.
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