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: Some kind of system of equations with double integrals

  1. Apr 17, 2007 #1
    Hey there, this is my first post, hopefully I don't screw anything up.

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

    Suppose that ∫ ∫D f(x, y) dA = 4 where D is the disk x2 +y2 ≤ 16. Now suppose E is the disk x2 + y2 ≤ 144 and g(x,y) = 3 f( [x/3], [y/3] ). What is the value of ∫ ∫E g(x, y) dA?

    2. Relevant equations

    3. The attempt at a solution

    Well, I figured switching the surface of integration into polar coordinates might be a good idea, but that didn't really lead anywhere. I figured that ∫ (0,4) f(x/3,y/3) would probably be 4/2pi since the limits of integration of the outside integral are usually 0 to 2pi and often have no variables in the function. I also noticed that the fuction in the second double integral was just multiplied by three but didn't know if I could just say that 3*f(x/3,y/3) was equal to f(x,y)... I'm thinking no. That's as far as my thinking went, I couldn't fathom where to go.
    Thanks for any help.
  2. jcsd
  3. Apr 17, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Just take the g integral and do the change of variables u=x/3, v=y/3. What does the domain look like in u,v variables?
  4. Apr 17, 2007 #3
    I'm afraid I don't follow what you mean by take the g integral and do the change of variables. Do I somehow take the g integral first? I think my biggest stumbling block is the lack of concrete numbers...

    and for the limits in x and y, would they be

    so u and v might be......

  5. Apr 17, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    Nooo. -12<x<12 so -4<u<4. But more concretely the u,v domain is your original disk D. Convert the g integral into something that looks like the f integral using the change of variables.
  6. Apr 18, 2007 #5


    User Avatar
    Science Advisor

    Don't worry about the limits of integration! If u= x/3 and v= y/3, then x= 3u and y= 3v. The circle x2+ y2= 144, in the "xy-plane" becomes (3u)2+ 3v2= 9u2+ 9v2= 144 or, dividing by 9, u2+ v2= 16, in the "uv-plane". Now do you see the point?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook