Results 1 to 4 of 4

Math Help - Improper Integrals

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    11

    Improper Integrals

    Evaluate the integral or state that it diverges:

    integral from 0 to 4 of dr/sqrt(4-r)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by smartartbug View Post
    Evaluate the integral or state that it diverges:

    integral from 0 to 4 of dr/sqrt(4-r)
     \int_0^4 \frac{1}{ \sqrt{4-r}}dr = -ln(4-r)_0^4 = -(ln(0) - ln(4))

    note that  ln(0) does not exist but

     \lim_{x \to 0 } ln(x) = - \infty

    Therefore this integral diverges
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    20
    Quote Originally Posted by AllanCuz View Post
     \int_0^4 \frac{1}{ \sqrt{4-r}}dr = -ln(4-r)_0^4 = -(ln(0) - ln(4))

    note that  ln(0) does not exist but

     \lim_{x \to 0 } ln(x) = - \infty

    Therefore this integral diverges
    lolwut...?

     \int_0^4 \frac{1}{ \sqrt{4-r}}dr

    let u=4-r therefore du=(-1)dx

     \int_4^0 \frac{1}{ \sqrt{u}}(-1)du

     -\int_4^0 \frac{1}{ \sqrt{u}}du

    \int_0^4u^{-\frac{1}{2}}du
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by DrDank View Post
    lolwut...?

     \int_0^4 \frac{1}{ \sqrt{4-r}}dr

    let u=4-r therefore du=(-1)dx

     \int_4^0 \frac{1}{ \sqrt{u}}(-1)du

     -\int_4^0 \frac{1}{ \sqrt{u}}du

    \int_0^4u^{-\frac{1}{2}}du
    oh **** I missed the square root...don't drink and integrate!
    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: June 5th 2011, 12:34 AM
  2. Improper Integrals 2
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 20th 2010, 09:59 PM
  3. improper integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 21st 2009, 06:04 PM
  4. Improper Integrals!!!!!!
    Posted in the Calculus Forum
    Replies: 17
    Last Post: June 21st 2008, 07:13 PM
  5. Improper Integrals (and one that isn't!)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 27th 2007, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum