1. Not finding help here? Sign up for a free 30min 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!

Average value of a curve

  1. Jan 22, 2006 #1
    If I had a sinusoid, how would I find the average value of it over a given interval. Say -pi/5 to pi/5 for instance. Thanks everybody.
     
  2. jcsd
  3. Jan 22, 2006 #2

    benorin

    User Avatar
    Homework Helper

    The average value of a function, say [tex]f(x),[/tex] over the interval [a,b] is given by the the formula

    [tex]f_{\mbox{ave}}=\frac{1}{b-a}\int_{x=a}^{b}f(x)dx[/tex]

    where I have assumed that [tex]f(x),[/tex] is properly integrable over [a,b].
     
  4. Jan 23, 2006 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The point is: if you had a constant function, f(x)= c, the "area under the curve" from a to b would f(x)(b-a)= c(b-a). With a variable function, that area is [tex]\int_a^b f(x)dx[/tex].

    If fave is the average of the function we must have
    [tex]\int_a^b f(x)dx= f_{ave}(b-a)[/tex]
     
  5. Jan 23, 2006 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The sine function is odd. Therefore the average over an interval symmetric around 0 will be 0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Average value of a curve
Loading...