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Find the volume of the solid?

  1. Feb 3, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2.

    2. Relevant equations
    None.

    3. The attempt at a solution
    This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I find the limits of integration for this double integral?
     
  2. jcsd
  3. Feb 3, 2015 #2

    Mark44

    Staff: Mentor

    Setting these integrals up is often the hardest part. Have you drawn a sketch of the solid?
     
  4. Feb 3, 2015 #3

    Ray Vickson

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    Please show you solution efforts. However, to help you start, here is a hint: when doing double or triple integral problems, always, always, always make a sketch of the integration region. It will help you figure out what your next steps should be.
     
  5. Feb 3, 2015 #4

    RUber

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    You can write z in terms of y and x in terms of y, so I would recommend y be your outer integral. Neither z nor x depend on eachother, so their order should not matter.
     
  6. Feb 3, 2015 #5

    jedishrfu

    Staff: Mentor

  7. Feb 3, 2015 #6

    LCKurtz

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    Neither of which is relevant to this problem.
     
  8. Feb 3, 2015 #7

    Svein

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    x=0, y=0, z=0 isn't a plane, it is a point. I expect you mean the plane y=0, z=0.
     
  9. Feb 3, 2015 #8

    LCKurtz

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    No, that is the three coordinate planes. He wrote what he meant there.
     
  10. Feb 3, 2015 #9

    Svein

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    Ah. Sorry.
     
  11. Feb 3, 2015 #10

    jedishrfu

    Staff: Mentor

    Yes that's true but the real point of the post was to tell the OP about a resource that would help him which was located near these references.
     
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