Results 1 to 2 of 2

Math Help - integration of an absolute value function??

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    21

    integration of an absolute value function??

    I'm very stuck on this problem because when I did it the way I thought it was supposed to be done I ended up with an answer of zero which definitely isn't possible... any tips on how to solve it would be greatly appreciated!!

    integral of... (|x+1| - |x-1|)dx

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by khood View Post
    I'm very stuck on this problem because when I did it the way I thought it was supposed to be done I ended up with an answer of zero which definitely isn't possible... any tips on how to solve it would be greatly appreciated!!

    integral of... (|x+1| - |x-1|)dx

    Thanks
    We know that |x|= \left\{ \begin{array}{rcl}<br />
-x & \mbox{if} & x<0 \\ 0 & \mbox{if} & x=0 \\<br />
x & \mbox{if} & 0<x<br />
\end{array}\right.. Now assuming integrability we integrate piecewise to get

    \int|x|dx=\left\{ \begin{array}{rcl}<br />
\frac{-x^2}{2}& \mbox{if} & x<0 \\ 0 & \mbox{if} & x=0 \\<br />
\frac{x^2}{2} & \mbox{if} & 0<x<br />
\end{array}\right.

    And we can see this corresponds to \frac{x|x|}{2}

    So we can conclude that \int|x|dx=\frac{x|x|}{2}+C

    Now just make the proper substiutions in your integral and you should get

    \frac{(x+1)|x+1|}{2}+\frac{(x-1)|x-1|}{2}+C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 1st 2011, 10:56 PM
  2. Absolute value integration.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 15th 2010, 11:30 PM
  3. Replies: 2
    Last Post: November 8th 2009, 02:52 PM
  4. Integration with absolute values?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 9th 2008, 03:45 AM
  5. Absolute Value Integration
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 11th 2008, 12:29 PM

Search Tags


/mathhelpforum @mathhelpforum