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!

Triple Integration for Volume

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid in the first octant bounded by the graphs of:
    z=1-y2
    y=2x
    x=3

    2. Relevant equations

    I was able to graph all three but I can't picture the region for integration. I'm not sure if I even have to graph it or if I can get my limits without the graph.

    3. The attempt at a solution
     
    Last edited: Nov 18, 2012
  2. jcsd
  3. Nov 18, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Please post an attempt at writing out the integral.
     
  4. Nov 18, 2012 #3
    After graphing the equations, I came up with:

    [itex]\int^{1}_{-1}[/itex] [itex]\int^{3}_{0}[/itex] [itex]\int^{1}_{0}[/itex] dzdxdy (this order was given as a hint)

    My final answer was 6?
     
  5. Nov 19, 2012 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, you need to put the given constraints as bounds in the integrals. The order needed also results from the dependencies in those bounds. The y bounds depend on x, and the z bounds depend on y, and therefore on x too. So the order should be z, y, x.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triple Integration for Volume
  1. Triple integral volume (Replies: 5)

Loading...