Results 1 to 4 of 4

Math Help - volume bounded by surface

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    6

    volume bounded by surface

    A volume in the first octant of space is bounded above by the surface z=4-(x^2), below by the plane z=0, and laterally by x=0 and the cylinder y=2x-(x^2). Compute the volume.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by ratedmichael View Post
    A volume in the first octant of space is bounded above by the surface z=4-(x^2), below by the plane z=0, and laterally by x=0 and the cylinder y=2x-(x^2). Compute the volume.
    \iint_A \int_0^{4-x^2} dz ~dA where A is the region of integration made by the parabola y=2x-x^2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    There's various ways to set it up.

    triple integral:

    \int_{0}^{2}\int_{0}^{2x-x^{2}}\int_{0}^{4-x^{2}}dzdydx

    Double integral:

    \int_{0}^{2}\int_{0}^{2x-x^{2}}(4-x^{2})dydx

    Try it in cylindrical or spherical.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2007
    Posts
    8

    Tough Solution

    Polar necessary?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume of Bounded region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2010, 01:37 AM
  2. volume bounded by ... rotated about x= -1
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 2nd 2010, 07:23 PM
  3. Volume (bounded by equations)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 28th 2010, 01:25 PM
  4. Replies: 0
    Last Post: February 23rd 2009, 05:34 PM
  5. Determine surface of area bounded by...
    Posted in the Calculus Forum
    Replies: 12
    Last Post: May 1st 2008, 09:24 AM

Search Tags


/mathhelpforum @mathhelpforum