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Homework Help: Triple integral finding bounds?

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

    Integrate the function over the solid given by the figure below (the bounding shapes are planes perpendicular to the x-y plane, a cone centered about the positive z-axis with vertex at the origin, and a sphere centered at the origin), if P=(0,0,5),Q=(0,4,3), and R=(sqrt(6),sqrt(10),0) .

    https://instruct.math.lsa.umich.edu/webwork2_course_files/ma215-f08/tmp/gif/homework8b-prob1-pimages/sfig16-8-1g4.gif [Broken]

    2. Relevant equations

    3. The attempt at a solution
    planes perpendicular to the x-y plane are the x-z plane and the y-z plane

    how do you use the figure to get the bounds for x,y,z

    I think that x is from 0 to R
    then y is from 0 to 4
    and z is from 0 to 5

    is this correct? do I need to switch to spirical coordinates?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Nov 1, 2008 #2


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    Welcome to PF!

    Hi beallio! Welcome to PF! :smile:

    No, "planes perpendicular to the x-y plane" means the y-z plane and the vertical plane through R.

    The top surface is part of a sphere, and the "front surface" is also curved … it's the cone through Q.

    Hint: divide the solid into horizontal slices of thickness dz, and integrate over z (split the integration into two parts … one below Q, and one above Q, since they'll be different functions). :wink:
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