Results 1 to 2 of 2

Math Help - Leibniz' rule

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    53

    Leibniz' rule

    hello,

    i am trying to evaluate

    =lim(as x -->2) of {[1/(x-2)][integral from 2 to x of [(sint)/t]dt]}

    i have tried with Leibniz' rule and now derived that

    z= [integral from 2 to x of (sinx/x)dt} =>

    dz/dx = (sinx)/x => z = integral of (sinx)/x

    but then i am still at a loss as to how to evaluate

    =lim(as x -->2) of {[1/(x-2)][integral of [(sinx)/x]dx]}



    Pleasssssssseeeeeeee hlp
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by pepsi View Post
    hello,

    i am trying to evaluate

    =lim(as x -->2) of {[1/(x-2)][integral from 2 to x of [(sint)/t]dt]}

    i have tried with Leibniz' rule and now derived that

    z= [integral from 2 to x of (sinx/x)dt} =>

    dz/dx = (sinx)/x => z = integral of (sinx)/x

    but then i am still at a loss as to how to evaluate

    =lim(as x -->2) of {[1/(x-2)][integral of [(sinx)/x]dx]}



    Pleasssssssseeeeeeee hlp
    Bottom line, you need:

    \lim_{x\rightarrow 2}\frac{1}{x-2}\int\limits_2^x\frac{\sin t}{t}\,dt=\lim_{x\rightarrow 2}\frac{\int\limits_2^x\frac{\sin t}{t}\,dt}{x-2}

    As both numerator and denominator are derivable in a neighborhood of 2 and we get an indeterminate of the form \frac{0}{0} , you can try L'Hospital, remembering that \int\limits_2^x\frac{\sin t}{t}\,dt=F(x)-F(2)\,,\,\,with\,\,F(t)'=\frac{\sin t}{t}

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Leibniz rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 8th 2011, 05:07 AM
  2. using Leibniz Rule
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 4th 2011, 10:39 PM
  3. The inverse of Leibniz's rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 20th 2010, 11:31 PM
  4. Leibniz' rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 5th 2009, 07:47 AM
  5. Example of Leibniz rule for integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 6th 2008, 09:53 AM

Search Tags


/mathhelpforum @mathhelpforum