1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

∫x*lnx*dx homework help

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    find the derivative of x*lnx
    and hence find
    ∫x*lnx*dx

    3. The attempt at a solution
    the derivative is 1+lnx
    the integral (by parts) i worked out to be x^2 * ln(x-1/2) / 2 + c

    but i dont know how you find the integral from the derivative.
    help?
    also is my integration by parts correct?

    please and thankyou
     
    Last edited: Mar 31, 2009
  2. jcsd
  3. Mar 31, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Re: ∫x*lnx*dx

    "find the derivative of x*lnx*dx"
    What is x*ln(x)*dx?

    ∫x*lnx*dx is a function, whose derivative is x*ln(x).
    x*lnx is a function, whose derivative is 1 + ln(x).

    As for your integration by parts, how on earth did you manage to change ln(x) to ln(x - 1/2) ?
     
  4. Mar 31, 2009 #3
    Re: ∫x*lnx*dx

    both were typos
    my bad

    there should be no .dx for the derivative
    and the integral should be x^2(lnx - 1/2) / 2 + c

    oops

    sorry

    now will anyone answer my question?
     
  5. Mar 31, 2009 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: ∫x*lnx*dx

    The question is asking you to use the fact that [itex]\frac{d}{dx}(x \ln x) = 1+\ln x[/itex] in calculating [itex]\int x \ln x\,dx[/itex].

    How did you do your integration by parts?
     
  6. Mar 31, 2009 #5
    Re: ∫x*lnx*dx

    how do you use that fact!!!!

    i went u=lnx u'=1/x
    v'=x v=x^2/2
    ∫x*lnx*dx=x^2lnx / 2 - ∫x^2/2x
    x^2lnx / 2 - ∫x/2
    x^2lnx / 2 - x^2/4
    rearange
    X^2 * (lnx - 1/2)*1/2
     
  7. Mar 31, 2009 #6

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: ∫x*lnx*dx

    If I told you that I would be telling you how to solve the problem.

    Knowing f(x) and its derivative f'(x), how would you compute ∫ f(x) dx via integration by parts?
     
  8. Mar 31, 2009 #7
    Re: ∫x*lnx*dx

    but for parts u only need the derivative of lnx not x*lnx
     
  9. Mar 31, 2009 #8

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: ∫x*lnx*dx

    You are supposed to use the derivative of x*ln(x) to aid in the calculation of ∫ x*ln(x) dx. Yes, you can calculate this integral by other means. However, in doing so you will not be doing what was asked of you and you will get minimal points as a result.

    The rules of this site (very good rules) prohibit me from giving you the solution. I can however ask some very leading questions. You have not answered my question from post #6:

    Knowing f(x) and its derivative f'(x), how would you compute ∫ f(x) dx via integration by parts?
     
  10. Apr 1, 2009 #9

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi brandy! :smile:
    Well, you obviously need to put (1 + lnx) in there somewhere, before you start. :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: ∫x*lnx*dx homework help
  1. Homework help (Replies: 1)

  2. Homework help (Replies: 2)

  3. Homework Help! (Replies: 4)

Loading...