Setting bounds for a double integral in polar coordinates

[dwn]

Homework Statement

Image attached

Homework Equations

r²=x²+y²

The Attempt at a Solution

∫∫ re^{-r^2} drdΘ

I'm not sure how to establish the boundaries. This is an online class so if you can offer any additional tips for evaluating types of integrals of this sort, that would be great. Thank you.

 

[haruspex]

I'm not sure how to establish the boundaries.

Try to graph the region.
If you want to approach it purely algebraically, the bounds are 0 < x < 1, 0< y < √(1-x²). Substitute the polar forms for x and y.