1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Average Value Question

  1. May 6, 2007 #1
    1. The problem statement, all variables and given/known data

    http://img296.imageshack.us/img296/7923/img0192re9.jpg [Broken]

    3. The attempt at a solution

    Hope you can see what I've written on the top of the page, but basically I want to find the antider. of f(x) from 1 to 4 (from the graph I suppose). So that should be the negative area under the graph plus the little triangle just above the x axis?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. May 6, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    Break it up into 2 integrals,
    [tex]\int^{3.5}_1 f(x) dx + \int_{3.5}^4 f(x) dx[/tex]

    We can see the 1st integral is just the negative of a trapezium, and it is -7/4.
    The 2nd integral is just a triangle, area 1/4. So the integral evaluates to -1.5.

    A better way to have done it would have been to see the area from 3 to 3.5 and 3.5 to 4 cancel out making the integral [tex]\int_1^3 f(x) dx[/tex], which is -3/2 as expected. Turns out you don't see an anti derivative, but if you were really really desperate, you could have written a piece wise definition of f(x) where f(x) = -x+1 for x between 0 and 2, f(x)=-1 for x between 2 and 3, so on, so forth..and done it the long way.

    Anyway, we have the integral now, you can do the rest.
  4. May 6, 2007 #3
    So basically average value = (1/3)*(-3/2)
    = -1/2
  5. May 6, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    Exactly. Good Work.
  6. May 6, 2007 #5
    *bows down to maths god*
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Average Value Question Date
Finding the Average Value of a Function Jan 29, 2018
Statistics average value question Aug 15, 2017
Average value of function Apr 9, 2016
Multivar; Path length, and average y-value over it Feb 10, 2016
Average speed question Jan 26, 2016