# Double Integral - Polar Coordinates

## 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.

Last edited:

## Answers and Replies

Related Calculus and Beyond Homework Help News on Phys.org
You'll have to express dxdy in other variables, and the intervals have to be changed.

How can I change them to polar coordinates?

Last edited:
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.