Results 1 to 2 of 2

Math Help - Leibnez Rule

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    147

    Leibnez Rule

    Hi all, I have to solve the following problem:

    Find dV/dt, where:

     \int_0^{t^2} (x+at)dF(x) where F(x) is the cdf of x on [0,  \infty ) and f(x) is its corresponding pdf.

    My question is can I just use Leibnez rule as one normally would, or does the whole cdf thing complicate matters? My senses tell me its the former.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298
    If "F(x) is the cdf of x on [0,) and f(x) is its corresponding pdf" then dF(x)= f(x)dx so the integral is
    \int_0^t^2(x+ at)f(x)dx and its derivative, by the Leibniz rule, is simply 2t(t^2+ at)f(t^2).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] quick question on product rule and equality rule for logs
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: October 19th 2011, 07:29 PM
  2. Replies: 5
    Last Post: October 19th 2009, 01:04 PM
  3. Replies: 3
    Last Post: May 25th 2009, 06:15 AM
  4. Replies: 2
    Last Post: December 13th 2007, 05:14 AM
  5. Replies: 3
    Last Post: August 31st 2006, 09:08 AM

Search Tags


/mathhelpforum @mathhelpforum