Results 1 to 2 of 2

Math Help - Average Value Function and Equivalent Periodic Function

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    4

    Average Value Function and Equivalent Periodic Function

    This is a homework problem and I'm not even sure where to start with it. The problem reads: "Show that if f(x) has period p, the average value of f is the same over any interval of length p. Hint:  \int_a^{a+p}f(x) dx as the sum of two integrals (a to p, and p to a+p) and make the change of variable x = t+p in the second integral."

    Okay so I know how to write the hint out and I get the point that f(t+p) = f(t) but what am I actually supposed to write out? I don't know out to transform this integral. Where do I start after writing out the 'hint'?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,413
    Thanks
    1852
    So you have gotten to
    \int_a^{a+p} f(x) dx= \int_a^p f(x)dx+ \int_p^{a+p} f(x)dx
    and then let x= t+ p (or t= x- p) to get
    \int_a^p f(x)dx+ \int_0^a f(t+p)dt= \int_a^p f(x)dx+ \int_0^a f(t)dt.

    But now, since the "x" and "t" in the integrals are "dummy variables" (they don't appear in the final integral so we can change letters at will), we can write that as
    \int_a^p f(x)dx+ \int_0^a f(x)dx

    Now, put those integrals back together into one integral.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of a periodic function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 17th 2011, 12:27 PM
  2. function is periodic
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 29th 2010, 01:45 PM
  3. Problem with periodic function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 6th 2010, 08:15 PM
  4. Periodic Function problem
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 27th 2007, 03:35 PM
  5. Periodic Function
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 29th 2006, 06:36 AM

Search Tags


/mathhelpforum @mathhelpforum