# Double Integral - Polar Coordinates

1. Apr 13, 2009

### duki

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

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. Apr 14, 2009

### _Andreas

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

3. Apr 14, 2009

### duki

How can I change them to polar coordinates?

Last edited: Apr 14, 2009
4. Apr 14, 2009

### _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.