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Using triple integrals

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data

    Use a triple integral to find the volume of the region. Below x+2y+2z=4, above z=2x, in the first octant.

    2. Relevant equations

    V=∫∫∫dV=∫∫∫dxdydz


    3. The attempt at a solution

    I have no clue where to begin as to finding those darn limits to integrate with. I'm sure I can evaluate the integral just fine, but I need help finding limits.
     
  2. jcsd
  3. Apr 1, 2012 #2
    Well, after plotting those two equations into my mac grapher app, it seems my y-limits could be from 0 to 2. But I'm unsure as to finding my x and z limits.
     
  4. Apr 1, 2012 #3
    Any assistance would be greatly appreciated. Thanks.
     
  5. Apr 1, 2012 #4

    SammyS

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    Patience, please.

    (Look at the rules for posting on this Forum, especially as regards "bumping" your thread.)
     
  6. Apr 1, 2012 #5

    SammyS

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    Where do the planes, x+2y+2z=4, and, z=2x, intersect?

    Where does each of those planes intersect the coordinate axes?
     
  7. Apr 1, 2012 #6
    Well, z=2x goes through the entire the y-axis, but doesn't intersect any other axes. x+2y+2z=4 intersects axes at x=4, y=2, and z=2.

    The two planes intersect at 2y+5x=4.

    But what's your point? What do I get out of this?
     
  8. Apr 1, 2012 #7

    SammyS

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    I should have asked, "Where does each of those planes intersect the coordinate planes?"

    The intersection of the two planes is a line. The equation, 2y+5x=4, specifies a plane !
     
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