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Double Integral - Polar Coordinates

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate by changing to polar coordinates

    2. Relevant equations

    Can't figure out how to make the integral stop after the sqrt(9-x^2)
    [tex]\int_0^\frac{3}{\sqrt(2)} \int_x^{\sqrt(9-x^2)} e^-(x^2+y^2) dy dx[/tex]

    3. The attempt at a solution

    I'm not sure where to really start on this one. I know it will end up being e^-r^2 but beyond that I'm not sure.
     
    Last edited: Apr 14, 2009
  2. jcsd
  3. Apr 14, 2009 #2
    You'll have to express dxdy in other variables, and the intervals have to be changed.
     
  4. Apr 14, 2009 #3
    How can I change them to polar coordinates?
     
    Last edited: Apr 14, 2009
  5. Apr 14, 2009 #4
    First of all: Draw a figure in the xy-plane with to see what shape the domain yields (probably something like a circle sector). Then you should be able to figure out what values you should give [tex]r[/tex] and [tex]\phi[/tex]. You usually substitute [tex]r*drd\phi[/tex] for [tex]dxdy[/tex] when using polar coordinates. However, the exact expression depends on what shape the domain yields.
     
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