Results 1 to 2 of 2

Math Help - Triple integral (spherical coordinate)

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    151

    Triple integral (spherical coordinate)

    find the volume of the solid D that lies above the cone z = (x^2 + y^2)^1/2
    and below the sphere z = (x^2 + y^2 + z^2)

    i've done the integration until i need to substitute cos phi = u..
    however.. i dont know to change the range..
    Triple integral (spherical coordinate)-spherical.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7

    Re: Triple integral (spherical coordinate)

    If u = \cos\phi then u = \cos0 = 1 when \phi=0, and u = \cos(\pi/4) = 1/\sqrt2 when \phi = \pi/4. That gives V = -\frac{2\pi}3\int_1^{1/\sqrt2}u^3\,du. From there, the best thing to do is probably to switch the limits of integration, which changes the sign of the integral and leads to V = \frac{2\pi}3\int^1_{1/\sqrt2}u^3\,du. That should be easy enough to integrate.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple Integral in Spherical Coordinates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 6th 2010, 05:58 PM
  2. Triple integral in spherical coordinates
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 23rd 2010, 12:00 PM
  3. Spherical Coordinate Triple Integral Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 3rd 2010, 11:08 AM
  4. Replies: 2
    Last Post: December 11th 2009, 05:50 AM
  5. Triple Integral in Spherical Coords.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 22nd 2009, 06:11 AM

Search Tags


/mathhelpforum @mathhelpforum