1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Evaluate the following triple integral

  1. May 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following triple integral

    [tex]I = \int\int\int_{R}x dv[/tex]

    in Cartesian coordinates where R is the finite region bounded by the surfaces z=0, y=x^3, y=8, z=x. Sketch the region R. Here dV is the element of volume.
    2. Relevant equations

    3. The attempt at a solution
    What I'm having trouble with is setting up the limits of integration.

    I already have
    0 < z < x
    x^3 < y < 8

    but what about x?

    And how do I know that the y and z limits are that way around and not x < z < 0 and 8 < y < x^3 instead?
  2. jcsd
  3. May 20, 2009 #2


    User Avatar
    Science Advisor

    Those inequalities do NOT describe a bounded region. Aren't there additonal restrictions?
  4. May 20, 2009 #3
    Hello Caesius.

    May I make a suggestion I think would be helpful to you?

    Suppose all you had to do was to plot the surfaces. Never mind (for now) the integration. Could you do that, nicely? The surface z=0 is just the x-y plane right. The surface y=x^3 is a paraboloid sheet, and z=x is a diagonal flat sheet. Suppose that was the only assignment, draw these three surfaces together, transparently so you could see where they intersect, and do it nicely. Then study them, closely, rotate the figure around interactively (you can do that in Mathematica), note the intersections, then go through the algebra proving your observations, then come back and answer your question. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook