Results 1 to 2 of 2

Math Help - double integrals and changing order of integration

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    14

    double integrals and changing order of integration

    \int_{-3}^1\int_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}}\: x^2 \: dxdy


    I think the domain for this is the shaded green:


    When I try to integrate as is, I wind up making it even more complicated so another method to solve this would be to change the order of integration, but if I were to do that I think I would have to split the domain up into parts. The problem is I'm not quite sure how to split this up, or if the above domain is even correct.

    Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by chewitard View Post
    \int_{-3}^1\int_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}}\: x^2 \: dxdy


    I think the domain for this is the shaded green:


    When I try to integrate as is, I wind up making it even more complicated so another method to solve this would be to change the order of integration, but if I were to do that I think I would have to split the domain up into parts. The problem is I'm not quite sure how to split this up, or if the above domain is even correct.

    Any help would be greatly appreciated.
    Dear chewitard,

    \displaystyle\int_{-3}^1\displaystyle\int_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}}\: x^2 \: dxdy=\displaystyle\int_{-3}^1\left[\frac{x^3}{3}\right]_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}}dy

    \displaystyle\int_{-3}^1\displaystyle\int_{-\sqrt{9-y^2}}^{\sqrt{9-y^2}}\: x^2 \: dxdy=\displaystyle\int_{-3}^{1}{\frac{2}{3}\sqrt{9-y^2}}dy

    Substitute y=3\sin{\theta} and you will be able to find the answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 8th 2011, 04:59 PM
  2. Double integrals changing order of integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 6th 2010, 01:33 AM
  3. Replies: 2
    Last Post: December 1st 2009, 01:29 PM
  4. Double Integrals - Order of Integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2009, 12:02 PM
  5. changing the order of integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 14th 2009, 06:47 AM

Search Tags


/mathhelpforum @mathhelpforum