Double Integral - Polar Coordinates

[duki]

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)
$$\int_0^\frac{3}{\sqrt(2)} \int_x^{\sqrt(9-x^2)} e^-(x^2+y^2) dy dx$$

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.

 

[_Andreas]

You'll have to express dxdy in other variables, and the intervals have to be changed.

 

[duki]

How can I change them to polar coordinates?

 

[_Andreas]

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 $$r$$ and $$\phi$$. You usually substitute $$r*drd\phi$$ for $$dxdy$$ when using polar coordinates. However, the exact expression depends on what shape the domain yields.