Results 1 to 6 of 6

Math Help - how do i integrate and go about doing this?

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    9

    how do i integrate and go about doing this?

    don't know hot to integrate and do this question. I integrated it by parts then got to integrate (x^2/ 2 + 2x^2) again..

    Attached Thumbnails Attached Thumbnails how do i integrate and go about doing this?-nummethods.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Not sure what you mean, but parts is right (for question a). Integrate x, differentiate arctan x, then integrate 1/2 x^2 all over 1 + x^2, which is equal to

    \frac{1}{2}\ \frac{1 + x^2 - 1}{1 + x^2}

    which you can split into

    \frac{1}{2}\  -\ \frac{1}{2}\ \frac{1}{1 + x^2}

    Just in case a picture helps...



    More in a tic
    Last edited by tom@ballooncalculus; April 22nd 2010 at 10:55 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    9
    Quote Originally Posted by tom@ballooncalculus View Post
    Not sure what you mean, but parts is right (for question a). Integrate x, differentiate arctan x, then integrate 1/2 x^2 all over 1 + x^2, which is equal to

    \frac{1}{2}\ \frac{1 + x^2 - 1}{1 + x^2}

    which you can split into

    \frac{1}{2}\  -\ \frac{1}{2}\ \frac{1}{1 + x^2}

    Just in case a picture helps...



    More in a tic
    how did you go about integrating 1/2 x^2 all over 1 + x^2, ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Quote Originally Posted by mistry88 View Post
    how did you go about integrating 1/2 x^2 all over 1 + x^2, ?
    By re-writing the numerator in order to split it as shown above... and now below...



    Spoiler:





    ... is the product rule. Straight lines differentiate downwards (integrate up) with respect to x.
    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2010
    Posts
    9
    re writing the numerator??

    sorry about my lack of knowledge
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    You know, the top bit.

    \frac{1}{2}\ \frac{x^2}{1 + x^2}

    =\ \frac{1}{2}\ \frac{1 + x^2 - 1}{1 + x^2}

    =\ \frac{1}{2}\ \frac{1 + x^2}{1 + x^2}\ -\ \frac{1}{2}\ \frac{1}{1 + x^2}

    =\ \frac{1}{2}\  -\ \frac{1}{2}\ \frac{1}{1 + x^2}

    It's a trick to by-pass long division, which you should nonetheless know.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrate 3 e^x
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 9th 2010, 01:16 PM
  2. how to integrate this ??
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 9th 2009, 08:14 PM
  3. Integrate
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 28th 2009, 07:54 PM
  4. How to integrate x^x?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2009, 07:51 PM
  5. Integrate
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 15th 2009, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum