Results 1 to 4 of 4

Math Help - Help with an multiple integral

  1. #1
    Junior Member
    Joined
    Feb 2007
    Posts
    70

    Help with an multiple integral

    I'm a little rusty when it comes to these kind of integrals. Any help would be appreciated.

    Find the indefinite integral of [(x^2 + y^2 - 2y^2)/(x^2 + y^2)^2]dx, that is, integrate with respect to x. I understand that I need to treat y as a constant, it's the integral itself that I'm having trouble with. Sorry if that's difficult to read, I still need to learn latex.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by spoon737 View Post
    I'm a little rusty when it comes to these kind of integrals. Any help would be appreciated.

    Find the indefinite integral of [(x^2 + y^2 - 2y^2)/(x^2 + y^2)^2]dx, that is, integrate with respect to x. I understand that I need to treat y as a constant, it's the integral itself that I'm having trouble with. Sorry if that's difficult to read, I still need to learn latex.
    i believe you have a typo or something here. they would not say y^2 - 2y^2, they'd just write -y^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2007
    Posts
    70
    Oops, you're right, that should read -y^2 instead of y^2 - 2y^2. This isn't how the actual problem was presented, I had to do some work to get to this point. I just forgot to simplify that one part. Still, I could use help in solving that integral.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by spoon737 View Post
    Oops, you're right, that should read -y^2 instead of y^2 - 2y^2. This isn't how the actual problem was presented, I had to do some work to get to this point. I just forgot to simplify that one part. Still, I could use help in solving that integral.
    Sorry for taking so long, here:

    I will start you off (remember, we are treating y as a constant throughout the entire problem)


    \int \frac {x^2 - y^2}{(x^2 + y^2)^2} dx

    We employ the method of partial fractions:

    \frac {x^2 - y^2}{(x^2 + y^2)^2} = \frac {A}{x^2 + y^2} + \frac {B}{(x^2 + y^2)^2}

    \Rightarrow x^2 - y^2 = A(x^2 + y^2) + B ...i think you know how to solve this, let's get to the meat of the matter

    \Rightarrow A = 1 \mbox { and } B = -2y^2

    \Rightarrow \int \frac {x^2 - y^2}{(x^2 + y^2)^2}dx = \int \frac {1}{x^2 + y^2}dx + 2y^2 \int \frac {1}{(x^2 + y^2)^2}dx

    now just find the integrals on the right: factor out the y^2 on the bottom of the first so you will get it in the form to use arctan, for the second, use trig substitution, x = ytan \theta

    If you get stuck you can check back with me
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with a multiple integral
    Posted in the Calculus Forum
    Replies: 15
    Last Post: December 6th 2011, 07:07 PM
  2. Multiple integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 10th 2008, 10:05 AM
  3. Multiple integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 17th 2008, 12:14 PM
  4. Multiple integral
    Posted in the Calculus Forum
    Replies: 10
    Last Post: July 16th 2008, 11:01 AM
  5. multiple integral
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 6th 2008, 09:58 PM

Search Tags


/mathhelpforum @mathhelpforum