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Determining double integral limits

  1. Feb 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Evaluate [itex] \iint\limits_S \vec{A} . \vec{n} ds[/itex] over the plane [itex] x^{2}+y^{2}=16[/itex], where [itex]\vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k} [/itex] and S is a part from the plane and R was projected over xz-plane.

    2. Relevant equations

    Surface Integral and Double Integration.

    3. The attempt at a solution

    This is an answered problem, but I didn't get how to determine the integration limits

    I understand that I have to integrate with respect to x and z due the fact the region is projected over "xz-plane", and I've to get the limits from the plane equation.

    The limits integration in the solution are [itex] \int_0^5 \int_0^4 dz dx [/itex]
  2. jcsd
  3. Feb 14, 2014 #2


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    ##x^2+y^2=16## is not a plane. It's a circular cylinder standing on the xy plane. And you haven't told us how high it goes in the z direction. Draw a picture to see what its projection on the xz plane would look like.
  4. Feb 15, 2014 #3
    And that's what confusing me, there's no height. So the problem is wrong, isn't?
  5. Feb 15, 2014 #4


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    I can't make sense of the problem statement. What is R? Is this quoted word for word?
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