Results 1 to 4 of 4

Math Help - definite integration

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    51

    definite integration

    The integral of [ 1 / t^3 * sqrt(t^2 - 1) ] from sqrt(2) to 2.
    Can someone help me in getting the integral..

    I tried u substitution but got stuck..

    u = sqrt(t^2-1)
    du/dt = (1/2)(sqrt(t^2-1)^-(1/2)
    du = " " * dt

    dV = t^3
    v = t^4/4

    Is this the right way? I get stuck after I rewrite it..

    is there an easier way, thank you
    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 xfyz View Post
    The integral of [ 1 / t^3 * sqrt(t^2 - 1) ] from sqrt(2) to 2.
    Can someone help me in getting the integral..

    I tried u substitution but got stuck..

    u = sqrt(t^2-1)
    du/dt = (1/2)(sqrt(t^2-1)^-(1/2)
    du = " " * dt

    dV = t^3
    v = t^4/4

    Is this the right way? I get stuck after I rewrite it..

    is there an easier way, thank you
    how about trig substitution? t = \sec \theta

    that's what i immediately thought of when i saw it. i'll try it the integration by parts way to see if i have any luck with it
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2007
    Posts
    51
    Quote Originally Posted by Jhevon View Post
    how about trig substitution? t = \sec \theta

    that's what i immediately thought of when i saw it. i'll try it the integration by parts way to see if i have any luck with it
    sorry could you explain where you're getting t= sec(-)? Is this an identity or something?
    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 xfyz View Post
    sorry could you explain where you're getting t= sec(-)? Is this an identity or something?
    yes, it's from one of the formulas for "trigonometric substitution." it's in your text, you can look it up
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: September 2nd 2010, 12:27 PM
  2. Definite integration help.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2009, 11:06 AM
  3. Definite Integration
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 4th 2009, 11:09 PM
  4. Integration, definite
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 6th 2008, 09:12 PM
  5. Definite Integration
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 9th 2007, 03:49 AM

Search Tags


/mathhelpforum @mathhelpforum