1. Not finding help here? Sign up for a free 30min 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 Intergral Bounds Help

  1. Jun 10, 2008 #1
    Hi guys,
    Im currently revising for my exams and I encountered a problem I hope someone will be able to help me with.

    1. The problem statement, all variables and given/known data
    Find the volume of the region of space bounded by:
    The planes x=0, y=0, z=0, z=3-2x+y and the surface y=1-x^2


    2. Relevant equations
    [tex]\int \int \int _R 1\, dV[/tex]

    3. The attempt at a solution
    First I decided to integrate with respect to the z direction as I wouldn't have to worry about splitting up the region yet.

    [tex]\int \int \int _0 ^{3-2x+y} 1\, dz\, dy\, dx[/tex]

    [tex]= \int \int 3-2x+y\, dy \, dx[/tex]

    ok. But now I have a problem due to the surface y=1-x^2 cutting our region defined by the 4 planes. Can we split the region and choose our bounds like below?

    [tex]= \int _1 ^{3/2} \int _{1-x^2} ^{2x-3} 3-2x+y\, dy\, dx \; + \int _0 ^1 \int _0 ^{2x-3} 3-2x+y\, dy \, dx[/tex]

    Thanks.
     
  2. jcsd
  3. Jun 10, 2008 #2
    i have something simpler:

    say f(x,y) = 3-2x+y

    so now volume is

    int (0,1) . int (0, 1-x^2) f(x,y) dy.dx
     
  4. Jun 10, 2008 #3

    Defennder

    User Avatar
    Homework Helper

    If you can picture the region, the volume you want appears to be confined to the 2nd octant. For this, you'll want the limits of integration for y to be from 0 to 1-x^2. Why is any "splitting of region" necessary?
     
  5. Jun 10, 2008 #4
    Thanks for the reply rootX, Defennder

    Indeed you are both right.
    After scratching my head for a while I noticed I drew my diagram slightly wrong (I had the plane as z=3+2x-y lol) so my region projected onto the xy-plane was piece-wise defined.
     
    Last edited: Jun 10, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Triple Intergral Bounds Help
  1. Intergration help (Replies: 4)

  2. Intergral help (Replies: 2)

Loading...