Results 1 to 4 of 4

Thread: integration

  1. June 4th 2011, 04:03 AM #1
    Rine198
    Rine198 is offline
    Junior Member
    Joined
    Mar 2011
    Posts
    34

    integration

    how do i intergrate

    sqrt(t^2+t^4)dt?

    thanks!
    Follow Math Help Forum on Facebook and Google+
  2. June 4th 2011, 04:06 AM #2
    Prove It
    Prove It is offline
    MHF Contributor Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,259
    Thanks
    697
    \displaystyle \sqrt{t^2 + t^4} = \sqrt{t^2(1 + t^2)} = \sqrt{t^2}\sqrt{1 + t^2} = t\sqrt{1 + t^2}.

    So \displaystyle \int{\sqrt{t^2 + t^4}\,dt} = \int{t\sqrt{1 + t^2}\,dt} which you can solve making the substitution \displaystyle u = 1 + t^2.
    Follow Math Help Forum on Facebook and Google+
  3. June 4th 2011, 04:11 AM #3
    Rine198
    Rine198 is offline
    Junior Member
    Joined
    Mar 2011
    Posts
    34
    is it possible to do it by inspection?
    Follow Math Help Forum on Facebook and Google+
  4. June 4th 2011, 04:13 AM #4
    Prove It
    Prove It is offline
    MHF Contributor Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,259
    Thanks
    697
    Quote Originally Posted by Rine198 View Post
    is it possible to do it by inspection?
    If you can recognise the function that differentiates to give \displaystyle t\sqrt{1 + t^2}, otherwise, just use the substitution...
    Follow Math Help Forum on Facebook and Google+
« using divergence theorem to prove Gauss's law | integration by substitution »

Similar Math Help Forum Discussions

  1. Integration help please these are three small even basic integration problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 3rd 2010, 12:54 AM
  2. sketch the region of integration and change the order of integration.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 2nd 2010, 04:57 AM
  3. Definite Integration - Double integration by parts
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 2nd 2010, 12:27 PM
  4. Simple Integration problem: Trigonometric Integration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 19th 2010, 10:55 AM
  5. Tricky integration, possibly Integration Factor
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 25th 2009, 06:58 AM

Search Tags


/mathhelpforum @mathhelpforum