Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Having trouble with a surface integral

  1. Jun 1, 2009 #1
    I'm self learning and working my way through the book "Div Grad Curl and All That". On one of the pages (27) the author says
    [tex] \int_{ }^{ } \int_{ }^{ } z^2 dS = \int_{ }^{ } \int_{ }^{ } \sqrt[ ]{ 1 - x^2 - y^2 } dx dy[/tex]

    "This is an ordinary double integral, and you should verify that its value is pi / 6.

    The hint was to convert to polar coordinates and the furthest I got was

    [tex] \int_{0}^{ \pi/2} \int_{0}^{1} \sqrt[ ]{ 1 - r^2cos^2( \theta) - r^2sin^2(\theta) } r dr d\theta[/tex]

    Any ideas getting past this point?
     
  2. jcsd
  3. Jun 1, 2009 #2

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    What's cos(theta)^2 + sin(theta)^2?
     
  4. Jun 1, 2009 #3
    =(

    So obvious!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Having trouble with a surface integral
  1. Having trouble (Replies: 2)

Loading...