Results 1 to 5 of 5

Math Help - Double integration

  1. #1
    Member
    Joined
    Jul 2007
    Posts
    151

    Question Double integration

    Use double integration to find the volume of the solid that is common to the cylinders x^2 + y^2 =25 and x^2 + z^2 = 25.

    Thank you very much.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    You could find the volume of one octant and then multiply by 8.

    8\int_{0}^{5}\int_{0}^{\sqrt{25-x^{2}}}\sqrt{25-x^{2}}dydx

    = 8\int_{0}^{5}(25-x^{2})dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2007
    Posts
    151
    Hi galactus,

    thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by kittycat View Post
    Hi galactus,

    thank you very much for your reply. Why multiple by 8? Could you please explain to me? Thanks.
    He used symmetry.

    The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by ThePerfectHacker View Post
    He used symmetry.

    The shape was equally divided into the 8 octants. He chose only 1 octant and multiplied it by 8.
    Yes. See the graph below.
    Attached Thumbnails Attached Thumbnails Double integration-july16.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: September 2nd 2010, 01:27 PM
  2. Double Integration
    Posted in the Calculus Forum
    Replies: 11
    Last Post: May 7th 2010, 06:27 PM
  3. Double integration ftw!
    Posted in the Calculus Forum
    Replies: 11
    Last Post: April 8th 2009, 05:18 AM
  4. Double Integration --- help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 10th 2008, 09:44 AM
  5. double integration
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 18th 2008, 07:51 PM

Search Tags


/mathhelpforum @mathhelpforum