1. Not finding help here? Sign up for a free 30min 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!

Multiple integral change of variables

  1. Oct 15, 2011 #1
    Let R denote the region inside x^2 + y^2 = 1 but outside x^2 + y^2 = 2y with x=>0 and y=>0. Let u=x^2 + y^2 and v=x^2 + y^2 -2y. Compute the integral of x*e^y over the region D in the uv-plane which corresponds to R under the specified change of coordinates.

    I'm having trouble with this one. My first attempt at figuring out the new limits of integration yielded 0<=u<=1 and 0<=v<=u, which seems wrong to me. I'm also not sure how to change the integrand to make it a function of u and v.
     
  2. jcsd
  3. Oct 15, 2011 #2
    I'm still trying to work out the new limits of integration myself, but I think it might help to complete the square for the second condition...

    As for changing the function's variables, can you solve for y in terms of u and v? (Hint: What is u-v?)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Multiple integral change of variables
Loading...