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Need help solving definite integral

  1. Sep 29, 2009 #1
    I need help on this one


    [tex]
    \int_0^{100} \sqrt{x}ln{x}dx
    [/tex]


    I've tried integrating it by parts and ended up with the equation

    [(2/3)(x^3/2)(lnx) - (4/9)(x^3/2)] from 0 to 100

    However, I can't plug it in because there's no value of ln(0). So, I'm at a loss right now. Any idea on where to go from here?
     
  2. jcsd
  3. Sep 29, 2009 #2
    [tex]x^{\frac{3}{2}}\ln x = x^{\frac{1}{2}}(x\ln x)[/tex]

    [tex]Let ~u = \frac{1}{x}. ~~Then ~\lim_{x\rightarrow0}(x\ln x) = \lim_{u\rightarrow+\infty}\frac{\ln\frac{1}{u}}{u}[/tex]

    Or you might try xlnx = ln(xx) and use the limit of xx as x→0+
     
  4. Sep 29, 2009 #3

    lanedance

    User Avatar
    Homework Helper

    i think the integral is not well defined and you should be considering

    [tex]\stackrel{lim}{a \rightarrow 0} \int_a^{100} dx.\sqrt{x}.ln(x) [/tex]
     
  5. Sep 30, 2009 #4
    Thanks. That really helped.
     
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