Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By romsek

Math Help - Integration Involving Absolute Value

  1. #1
    Banned
    Joined
    Jan 2013
    From
    New York City
    Posts
    658
    Thanks
    7

    Integration Involving Absolute Value

    How does one integrate a function involving an absolute value?

    Here are two sample questions:

    Let INT = integrate

    (1) INT |2x-3| dx


    (2) INT |2x+3| dx

    For question 2, the lower limit of integration is 0 and the upper limit of integration is 2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,755
    Thanks
    1136

    Re: Integration Involving Absolute Value

    just break it into pieces using the appropriate, non absolute value, expression for the different intervals needed.

    for example |x| is -x on (-infinity, 0] and x on [0, infinity)

    |2x - 3| is (3 - 2x) on (-infinity, 1.5), and (2x - 3) on (1.5, infinity)
    Thanks from nycmath
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,857
    Thanks
    739

    Re: Integration Involving Absolute Value

    Hello, nycmath!

    The problem is rather silly.


    (2)\;\int^2_0 |2x+3|\,dx

    The graph of y \,=\,2x+3 looks like this.

    Code:
              |
              |   /
              |  /
              | /
             3|/
              *
             /|
            / |
        - -*- + - - -
          /   |
         /    |
    The graph of y \:=\:|2x +3| looks like this:

    Code:
              |
              |    /
              |   *
              |  /:
              | / :
             3|/  :
        \     *   :
         \   /|   :
          \ / |   :
          -*- + - + - -
              |   2
              |
    And we are to evaluate from 0 to 2.
    (We could have ignored the absolute values!)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Jan 2013
    From
    New York City
    Posts
    658
    Thanks
    7

    Re: Integration Involving Absolute Value

    From 0 to 2 forms a trapezoid.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Definite Integral Involving Absolute Value
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 14th 2010, 05:20 PM
  2. Inequality involving absolute value
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 26th 2009, 08:53 AM
  3. an absolute max and min problem involving e
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 26th 2009, 06:02 PM
  4. Limit involving Absolute Values.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 10th 2008, 11:24 AM
  5. inequality involving absolute value
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 27th 2006, 03:13 PM

Search Tags


/mathhelpforum @mathhelpforum