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Homework Help: Surface Integral

  1. May 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Find integral I = ∫∫xz^2 dydz + (x^2y − z^3) dzdx + (2xy + y^2z) dxdy (Integrate over A)
    if A is half a sphere(radius is a). Sphere is given with equation z=(a-x^2-y^2)^1/2 and z=0.

    2. Relevant equations
    The excercise is in 2 parts , find it with just integrating and b) applying gauss's law.

    3. The attempt at a solution
    I just cant understand how i get it ... Every way i can think of , gives me wrong answer, I have to find scalar. If i substitute x from the sphere equation , then in integration bounds it still remains ?
    I know this aint much to go on but help me. Just tell me what i can substitute so i can find this ingtegral or is it even possible ? I dont need whole excercise, i can integrate myself.
    sorry for bad english.
  2. jcsd
  3. May 10, 2013 #2


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    Science Advisor

    I would do this as three separate integrals: Doing the "dydz" integral y will go from -a to a and, for each y, z will go from 0 to [itex]\sqrt{a^2- y^2}[/itex]. And, of course, for each y and z, [itex]x= \sqrt{a^2- y^2- z^2}[/itex]. The first integral is
    [tex]\int\int xz^2 dydz= \int_{y=-a}^a\int_{z= 0}^\sqrt{a^2- y^2} z^2\sqrt{a^2- y^2- z^2}dzdy[/tex]
    and similarly for the other two integrals.
  4. May 10, 2013 #3
  5. May 11, 2013 #4
    Did it with spherical coordinates now . Tthis is so impossible :(
    http://www.upload.ee/image/3302135/20130511_041747.jpg [Broken]
    http://www.upload.ee/image/3302136/20130511_041718.jpg [Broken]
    Last edited by a moderator: May 6, 2017
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