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Double Integral - Polar Coordinates

  • Thread starter duki
  • Start date
  • #1
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Homework Statement



Evaluate by changing to polar coordinates

Homework 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]

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:

Answers and Replies

  • #2
144
1
You'll have to express dxdy in other variables, and the intervals have to be changed.
 
  • #3
264
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How can I change them to polar coordinates?
 
Last edited:
  • #4
144
1
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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