Results 1 to 4 of 4

Math Help - improper integrals!

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    14

    improper integrals!

    the integral from 0 to 1 of lnx/(x^1/2)


    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    You got a typo in the upper integration limit, fix it and then we'll talk.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by luckeyduck View Post
    the integral from 0 to 1 of lnx/(x^1/2)


    thanks!

    try integration by parts...

    u=ln(x) and dv=\frac{1}{\sqrt{x}}dx

    du=\frac{1}{x}dx and v=2\sqrt{x}

    so we get

    \int\frac{ln(x)}{\sqrt{x}}=2\sqrt{x}ln(x)-\int 2 \sqrt{x}\frac{1}{x}dx

    \int\frac{ln(x)}{\sqrt{x}}=2\sqrt{x}ln(x)-2\int x^{-1/2}dx


    You should be able to get it from here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    I'm pretty sure that luckeyduck is not ready to digest the following solution, but I'd like to show this attempt, since double integration tricks make (sometimes) these things easier:

    \begin{aligned}<br />
  \int_0^1 {\frac{{\ln x}}<br />
{{\sqrt x }}\,dx}  &=  - \int_0^1 {\int_x^1 {\frac{{dy\,dx}}<br />
{{y\sqrt x }}} }  \hfill \\<br />
   &=  - \int_0^1 {\underbrace {\int_0^y {\frac{{dx}}<br />
{{\sqrt x }}} }_{2\sqrt y }\,\frac{{dy}}<br />
{y}}  \hfill \\<br />
   &=  - 2\int_0^1 {\frac{1}<br />
{{\sqrt y }}\,dy}  \hfill \\<br />
   &=  - 4.<br />
\end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Improper Integrals
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: February 15th 2011, 12:09 AM
  2. improper integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 7th 2009, 05:06 AM
  3. Improper Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 17th 2009, 08:29 PM
  4. Improper Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 5th 2008, 11:57 AM
  5. Improper Integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 24th 2007, 05:05 PM

Search Tags


/mathhelpforum @mathhelpforum