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!

Integral homework problem help

  1. Apr 30, 2006 #1
    [tex]2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx[/tex]
    Can you help me with this integral?
     
  2. jcsd
  3. Apr 30, 2006 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You have already been advised to do a change of variables, rather than do this in Cartesian variables.
     
  4. Apr 30, 2006 #3
  5. Apr 30, 2006 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, how would you go about proving that the unit ball has volume [itex]\frac{4}{3}\pi[/itex] ?
     
  6. Apr 30, 2006 #5
    Well, the idea is probably good, but it doesn't help me with the integral
     
  7. Apr 30, 2006 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, the idea is just to use spherical coordinates. Have you sketched the region over which that integral is taken? Looks to me like there is a heckuvalot of symmetry there!
     
  8. May 1, 2006 #7
    Won't it be much more complicated, or is it the only way?
    r=(x^2+y^2+z^2)^1/2.
     
    Last edited: May 1, 2006
  9. May 1, 2006 #8
    It's clear that there is symmtry, but if r=(x^2+y^2+z^2)^1/2 everything will be much more complicated. How should it be solved then?
     
  10. May 1, 2006 #9
    Sorry for this post, I had some problems with my internet browser.
     
  11. May 1, 2006 #10

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    -=nobody=-, as everyone has already said on this thread, transform your coordinates. ie, set

    [tex] x= a r \cos\theta [/tex]

    [tex] y = b r\sin \theta [/tex]

    Now, find the Jacobian and limits of integration of [itex] \theta [/itex] and [itex] r [/itex]. Can you take it from here?
     
    Last edited: May 1, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Integral homework problem help
Loading...