Results 1 to 2 of 2

Math Help - Integration problem

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    71

    Integration problem

    I've worked through a long substitution question and have come to this point.

    t^2(du/dt) = 2te^(-u)

    I know I have to integrate both sides but am struggling with how to do it?!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    \displaystyle t^2\frac{du}{dt} = 2te^{-u}

    Let's start by cancelling t from both sides,

    \displaystyle t\frac{du}{dt} = 2e^{-u}

    Now we'll isolate the derivative as this may be separable.

    \displaystyle \frac{du}{dt} = \frac{2e^{-u}}{t}

    Seems we can now separate so,

    \displaystyle \frac{du}{2e^{-u}} = \frac{dt}{t}

    Neatening up a little

    \displaystyle \frac{1}{2}e^{u}~du = \frac{dt}{t}

    And integrating

    \displaystyle \int \frac{1}{2}e^{u}~du = \int \frac{dt}{t}

    \displaystyle \frac{1}{2}e^{u} = \ln (t)+C

    Finishing,

    \displaystyle e^{u} =  2\ln (t)+C

    \displaystyle u = \ln{( 2\ln (t)+C)}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 20th 2010, 06:46 PM
  2. Integration Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 5th 2010, 10:00 PM
  3. integration problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 23rd 2010, 05:03 AM
  4. Replies: 2
    Last Post: February 19th 2010, 11:55 AM
  5. Integration problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 19th 2009, 05:24 PM

Search Tags


/mathhelpforum @mathhelpforum