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: Substituting spherical coordinates to evaluate an integral

  1. Dec 1, 2015 #1
    I have to evaluate

    $$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$

    using spherical coordinates.

    This is what I have come up with

    $$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$

    by a combination of sketching and substituting spherical coordinates.

    After evaluating I obtain this integral to equal 3.57.

    where as the first one evaluates to 5.236.

    These are so difficult :(
  2. jcsd
  3. Dec 1, 2015 #2


    User Avatar
    Homework Helper

    I am not convinced you did that right.
    The volume of integration appears to be a sphere for z<0 and a cylinder for z>0. Your spherical integral doesn't look like that.

    Are you allowed to use spherical integral for the lower half and cylindrical integral for the upper half? Or maybe just geometry...1/2 volume of unit sphere + volume of unit cylinder = 5.236.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted