1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Polar coordinates to set up and evaluate double integral

  1. Dec 10, 2013 #1
    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

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

    and then my inside would become ∫[itex]^{\pi/2}_{-\pi/2}[/itex] ∫[itex]^{5}_{0}[/itex] (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. jcsd
  3. Dec 10, 2013 #2


    User Avatar
    Gold Member

    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.
  4. Dec 10, 2013 #3


    User Avatar
    Science Advisor

    What about [itex]u= r^2/2[/itex]?

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted