Results 1 to 3 of 3

Math Help - Integration problem

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    9

    Integration problem

    Once again I turn to this great forum for help. Could someone explain this for me?

    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
    I'm interested in the steps for this problem as well, can someone answer plz
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    First let y = sqrt(x). Then 2y dy = dx (after a little work.)

    So the integral becomes:
    Int[sqrt(x)/(x + 100) dx] = Int[2y^2/(y^2 + 100) dy] = 2*Int[y^2/(y^2 + 100) dy]

    Now for a trick add and subtract 100 in the numerator:
    2*Int[(y^2 + 100 - 100)/(y^2 + 100) dy] = 2*Int[(y^2 + 100)/(y^2 + 100) dy] + 2*Int[-100/(y^2 + 100) dy]

    = 2*Int[dy] - 200*Int[1/(y^2 + 100) dy] = 2*y - 20*cot^(-1)(10/y)

    = 2*sqrt(x) - 20*cot^(-1)(10/sqrt(x))

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: February 19th 2010, 11:55 AM
  2. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 22nd 2009, 12:03 PM
  3. problem in integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 23rd 2008, 10:59 AM
  4. integration problem no.11
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 22nd 2007, 05:02 AM
  5. integration problem no.10
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2007, 03:25 AM

Search Tags


/mathhelpforum @mathhelpforum