Results 1 to 4 of 4

Math Help - Integrating an ln() Function.

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    2

    Integrating an ln() Function.

    Hey, I need a help integrating an natural log function, as the title states. My teacher never taught it to the class and I am having a difficult time trying to understand it on other sites. My AB test is in 2 days and I am very worried about getting a low score. The question: v(t) = ln(1 + t^2) How far does the object travel between time t = 0 and time t = 10? When I put the integration of the function with limits 0 and 10, the calculator does not spit out the one number that I want. I have the TI-89 and when I put the MODE -> APPROX or when I (diamond) [ENTER] the equation, it still does not spit out one number. I would greatly appreciate help for both of my concerns
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,115
    Thanks
    992
    Quote Originally Posted by Acidicism View Post
    Hey, I need a help integrating an natural log function, as the title states. My teacher never taught it to the class and I am having a difficult time trying to understand it on other sites. My AB test is in 2 days and I am very worried about getting a low score. The question: v(t) = ln(1 + t^2) How far does the object travel between time t = 0 and time t = 10? When I put the integration of the function with limits 0 and 10, the calculator does not spit out the one number that I want. I have the TI-89 and when I put the MODE -> APPROX or when I (diamond) [ENTER] the equation, it still does not spit out one number. I would greatly appreciate help for both of my concerns
    put it back to AUTO mode ... then do "diamond" ENTER

    my TI-89 says \int_0^{10} \ln(1+t^2) \, dt = 29.093
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    771
    Hello, Acidicism!

    To integrate a function with \ln, "by parts" is usually needed.


    v(t) \:=\: \ln(t^2 + 1)
    How far does the object travel between time t = 0 and t = 10 ?

    By parts: . \begin{array}{ccccccc}u &=& \ln(t^2+1) & & dv & = & dt \\ \\[-4mm] du &=& \dfrac{2t\,dt}{t^2+1} & & v &=& t \end{array}

    Then: . \int\ln(t^2+1)\,dt \;=\;t\ln(t^2+1) \;- \int\frac{2t^2}{t^2+1}\,dt \;=\;t\ln(t^2+1) \;- \int\left[2 - \frac{2}{t^2+1}\right]\,dt

    . . = \;t\ln(t^2+1) - 2t + 2\arctan(t)\,\bigg]^{10}_0

    . . = \;\bigg[10\ln(101) - 2(10) + 2\arctan(10)\bigg] - \bigg[0\ln(1) - 2(0) + 2\arctan(0)\bigg]

    . . = \;10\ln(101) -20 + 2\arctan(10)

    . . = \;20.09346052...

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    2
    Oh, I just realized I integrated it with respect to x instead of t. Thanks sir. I don't really get this; why is there a t in front and why are you subtracting the integral of the stuff inside?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrating to produce a log function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 7th 2011, 03:29 AM
  2. Integrating this function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 11th 2009, 10:08 PM
  3. integrating a function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 14th 2009, 08:13 AM
  4. Integrating a function of compressibility
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 5th 2009, 07:28 AM
  5. Integrating this function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 27th 2008, 12:57 PM

Search Tags


/mathhelpforum @mathhelpforum