1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integral Xabs(x)

  1. Sep 29, 2007 #1
    1. The problem statement, all variables and given/known data
    integral of x|x|dx.. [-1,1]

    3. The attempt at a solution

    when graphing it, it is even (looks like the cubic function) and would be 0... but I am having problems convincing myself of this. i checked it out using my calculator, and it just gives back x|x|.. i know if you do the integral of abs x you would split it up into positive and negative parts and all that.. but this is obviously different since it goes below y=0...
  2. jcsd
  3. Sep 29, 2007 #2


    User Avatar

    You would still split it up and add the integral for x>0 up with the one for x<0.
  4. Sep 30, 2007 #3


    User Avatar
    Homework Helper

    I think you mean it's an odd function. And the definite integral from -a to a should give you zero.

    If you use the definition for absolute value,

    |x| = x for x => 0 , -x for x < 0 ,

    then your integrand is

    x·|x| = x^2 for x => 0 , -(x^2) for x < 0 .

    That will explain the graph and the result for your definite integral.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook