Results 1 to 2 of 2

Math Help - Double integral in polar coordinates 3

  1. #1
    Yan
    Yan is offline
    Member
    Joined
    May 2008
    Posts
    103

    Double integral in polar coordinates 3

    Use polar coordinates to find the volume of the given solid.

    Bounded by the paraboloids z=3x^2 + 3y^2 and z=4-x^2-y^2
    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
    3(x^{2}+y^{2})=4-(x^{2}+y^{2})

    3r^{2}=4-r^{2}

    r=\pm{1}

    \int_{0}^{2\pi}\int_{0}^{1}\int_{3r^{2}}^{4-r^{2}}rdzdrd{\theta}

    Here is the same in rectangular. That way you can see how they interchange.

    3x^{2}+3y^{2}=4-x^{2}-y^{2}

    Solve for y=\pm\sqrt{1-x^{2}}

    From this we can see x=\pm{1}

    So, we get \int_{-1}^{1}\int_{-\sqrt{1-x^{2}}}^{\sqrt{1-x^{2}}}\int_{3x^{2}+3y^{2}}^{4-x^{2}-y^{2}}dzdydx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Double Integral with Polar Coordinates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 8th 2011, 08:43 AM
  2. Double integral with polar coordinates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2011, 03:44 PM
  3. Double integral in polar coordinates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 16th 2010, 08:24 AM
  4. Double integral and polar coordinates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 27th 2008, 08:07 PM
  5. Double integral in polar coordinates 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 24th 2008, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum