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 integral of solid

  1. Jul 7, 2011 #1
    Find the volume of the solid that lies under the paraboloid z = x^2 + y^2, above xy plane,
    and inside the cylinder x^2 + y^2 = 2y

    First, i try to find the range..
    i transfer it to cylindrical coordinates..

    sqrt(y^2)=<z<=r^2
    i don't know how to find r
    i know that phi is from 0 to 2pi because it's paraboloid right?
    how am i going to eliminate y? because, y cannot exist in the cylindrical coordinate..
     
  2. jcsd
  3. Jul 7, 2011 #2

    lanedance

    User Avatar
    Homework Helper

    the outer r limit will be the cylinder, the inner r limit the parabliod, express the inner limit as r(z)

    the xy plane means the lower limit for z will be z=0

    phi will be from 0 to 2pi, as there is nothing in the problem to limit the angular range, so you must integrate over the whole range
     
  4. Jul 7, 2011 #3

    lanedance

    User Avatar
    Homework Helper

    don't forget the jacobian in the integral either
     
  5. Jul 7, 2011 #4
    got it!! thank u very much!! =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triple integral of solid
Loading...