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: Surface integral without using Gauss' theorem

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate §§ A.n dS if
    A= 2y(x^2)i-(y^2)j + 4xzk
    over the region in the first octant bounded by (y^2)+(z^2) = 9 and x = 2

    2. Relevant equations

    3. The attempt at a solution

    Let n = (yj + zk) / 3

    then A.n = [-(y^3) +4xz^3] / 3

    Since we 'll project the surface onto the xy-plane:
    |n.k| = z/3 and z = SQRT(9-y^2)

    Putting all together I obtain
    = §§R (4xz^3 - (y^3))/z dx dy

    Now making the appropriate changes and setting up the limits of integration:

    §y=30 §x=20 4x(9-y^2) - (y^3)/sqrt(9-y^2) dx dy

    However I always obtain 108 as a result and not 180 as my book suggested me (and after verification by Gauss' divergence theorem.

    Is there a problem with the limits of integration? Wrong projection? I really have no clue ...
    Thanks for the help!
  2. jcsd
  3. Sep 20, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    You've only calculated the integral over one side/face of the surface....there are three more faces that make up the closed surface bounding the given region...you need to calculate the surface integral over all 3 of those as well.
  4. Sep 20, 2009 #3
    Thanks a lot!
    I finally got it (at least I hope so ;-) !
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook