Results 1 to 3 of 3

Thread: antiderivative

  1. #1
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3

    antiderivative

    Say you want to write $\displaystyle \int^{x+ct}_{x-ct} g(x) \ dx = G(x+ct) - G(x-ct) $ (where $\displaystyle G $ is an antiderivative of $\displaystyle g$)

    for the odd 2-periodic function $\displaystyle g(x)=\left\{\begin{array}{ccc}-10,&\mbox{ if }
    -1 \le x<0 \\10, & \mbox{ if } 0 \le x <1 \\g(x+2L) & \text{otherwise}\end{array}\right.$

    then would G(x) be

    $\displaystyle G(x)=\left\{\begin{array}{ccc}-\int_{-1}^{x} 10 \ dx = -10x-10 \,&\mbox{ if }
    -1 \le x<0 \\ -\int_{-1}^{0} 10 \ dx + \int_{0}^{x}10 \ dx = -10 + 10x, & \mbox{ if } 0 \le x <1 \\F(x+2L) & \text{otherwise}\end{array}\right.$ ?


    You couldn't just write

    $\displaystyle G(x)=\left\{\begin{array}{ccc}-10x\,&\mbox{ if }
    -1 \le x<0 \\ 10x, & \mbox{ if } 0 \le x <1 \\F(x+2L) & \text{otherwise}\end{array}\right.$

    could you?
    Last edited by Random Variable; Feb 16th 2010 at 11:00 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    I made my question less abstract in hopes it makes sense to someone.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    If you look at the antidervative of g over a given interval (say -1,0), then you have g(t)=-10, which has -10x as an antiderivative
    So over this interval, $\displaystyle G(t)=-10(x)-(-10)(-1)=-10x-10$

    So no you can't write the last part you did. It would be like you integrate from 0 to x, which is false !
    It's easy to see that on a graph, since the integral is the area under the line at y=-10

    I don't know if it's clear... ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. antiderivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 20th 2009, 11:04 AM
  2. Antiderivative Help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Apr 16th 2009, 03:40 PM
  3. Antiderivative of 2^t
    Posted in the Calculus Forum
    Replies: 11
    Last Post: Apr 6th 2009, 07:00 PM
  4. Antiderivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 4th 2009, 05:31 AM
  5. Antiderivative (sin x)(ln x)
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Oct 6th 2008, 08:31 PM

Search Tags


/mathhelpforum @mathhelpforum