Results 1 to 3 of 3

Math Help - Convergent/Divergent Integral

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    10

    Convergent/Divergent Integral

    Evaluate the following integral if it is convergent.

    <br />
\int_1^{\infty}\frac{ln^2x}{x^3}dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member General's Avatar
    Joined
    Jan 2010
    From
    Kuwait
    Posts
    562
    Quote Originally Posted by zer0e View Post
    Evaluate the following integral if it is convergent.

    <br />
\int_1^{\infty}\frac{ln^2x}{x^3}dx
    \color{blue}\int_1^{\infty}\frac{ln^2x}{x^3}dx
    = \color{blue}\lim_{t\to\infty} \int_1^{t}\frac{ln^2x}{x^3}dx.

    To solve the integral, use integration by parts with \color{blue}u=ln^2(x) and \color{blue}dv=\frac{1}{x^3}dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    Of course we evaluate as long as having its convergence:

    For all x\ge1 is \ln x<\sqrt x, thus \ln^2x<x hence \frac{\ln^2x}{x^3}<\frac1{x^2}, and the integral converges since \int_{x\ge1}\frac{dx}{x^2}<\infty.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Improper integral (convergent/divergent)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 25th 2010, 03:47 PM
  2. Improper integral convergent or divergent?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 5th 2010, 12:47 PM
  3. Improper integral. Convergent or divergent?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 2nd 2010, 06:20 AM
  4. Help with convergent/divergent integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 01:16 PM
  5. Replies: 1
    Last Post: February 17th 2008, 04:12 PM

Search Tags


/mathhelpforum @mathhelpforum