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Triple integrals

  1. Oct 1, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the region bounded by z=x+y, z=10, and the planes x=0, y=0

    3. The attempt at a solution

    If I want to integrate with respect to z,y, then x;
    Then I think the limits of integration would be 0≤x≤z-y, so for x the be its largest, set y=0 and z to be large = 10, therefore, 0≤x≤10

    for y, keep x constant;
    0≤y≤z-x, for y to be large, z should be large, therefore 0≤y≤10-x

    and z is already given by the equations in the question; 10≤z≤x+y

    I'm not sure that these are right because I have a hard time picturing it in 3D??
    Also, Since no function was given, am i just integrating 1, or is a function supposed to be made from the equations in the question?
     
  2. jcsd
  3. Oct 1, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi mirandasatterley! :smile:

    No, integrating three times is not usually a sensible way to do it.

    To find a volume, divide into slices, find the area of each slice, and just integrate once.

    In this case, use horizontal slices (z = constant), of thickness dz, and integrate the area.
    The horizontal slices will be triangles.
    Yes. :smile:
     
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