Polar coordinates to set up and evaluate double integral

1. Dec 10, 2013

mikky05v

1. The problem statement, all variables and given/known data

Use polar coordinates to set up and evaluate the double integral f(x,y) = e-(x2+y2)/2 R: x2+y2≤25, x≥0

3. The attempt at a solution

First I just want to make sure I'm understanding this

my double integral would be

∫$^{\pi/2}_{-\pi/2}$ because x≥0 ∫$^{5}_{0}$ because my radius is 5 (e-(x2+y2)/2) r dr dθ

and then my inside would become ∫$^{\pi/2}_{-\pi/2}$ ∫$^{5}_{0}$ (e-r2/2) r dr dθ

can anyone confirm for me that this is correct and give me a brief break down on integrating.

obviously I would use substitution because I have r er2 but the -1/2 is throwing me a bit when it comes to the substitution.

Also how would i go about changing the limits while I'm substituting.
u= r2
du = 2r dr
isn't there something I have to do with my limits of integration that involves my u and du?

2. Dec 10, 2013

CAF123

Consider another u substitution. You don't have to explicitly change the bounds - you can just call them u1 and u2 midcalculation and then sub back in the r dependence at the end.

3. Dec 10, 2013

HallsofIvy

Staff Emeritus
What about $u= r^2/2$?

You can either, as CAF123 says, do the integration and then change back to r, or you can just replace the "r" limits with the corresponding "u" limits. When r= 0, what is u? When r= 5, what is u?