Results 1 to 2 of 2

Math Help - improper intergals

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    9

    improper intergals

    OK so i'm having trouble with two problems.

    first off

    \int_{0}^{2} \frac{1}{\sqrt{l x-1 l}} dx

    i know to split into two limits but i don't know what to do with the square root.

    second

    \int_{0}^{1} \frac{1}{2 \sqrt{x}} dx

    this one i don't really know where to start

    any help would be appreciated, Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    Because |x-1|=|1-x| is an 'even function' respect to 1 You need only to compute the first integral between 0 and 1 and then multiply by two. So it is...

    \int_{0}^{2} \frac{dx}{\sqrt{|x-1|}} = 2\cdot \int_{0}^{1} \frac{dx}{\sqrt{1-x}} = 2\cdot |-2\cdot \sqrt{1-x}|_{0}^{1} = 2\cdot 2 = 4

    The second integral is similar to the first but easier...

    \frac{1}{2} \int_{0}^{1}\frac {dx}{\sqrt{x}} = \frac{1}{2} \cdot |2\cdot \sqrt{x}|_{0}^{1} = \frac{1}{2}\cdot 2 = 1

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Improper Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 18th 2009, 07:35 PM
  2. Improper Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 17th 2009, 08:44 PM
  3. can u explain the basics of intergals?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 14th 2009, 04:25 PM
  4. improper int
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 24th 2008, 02:56 PM
  5. Improper:
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 12th 2007, 02:10 PM

Search Tags


/mathhelpforum @mathhelpforum