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!

Mean Value Theorem for Integrals

  1. Mar 8, 2006 #1
    Can someone please explain to me how to use this and give an example that we can walk through please? My book doesn't give an example of what it is talking about.

    ~Kitty
     
  2. jcsd
  3. Mar 8, 2006 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Your just talking about the theorem that if [itex]a \leq b[/itex], and f is continuous, then:

    [tex]
    \int_a^b f(t) \, dt = f(x) (b - a)
    [/tex]

    has a solution for x in the range [itex]a \leq x \leq b[/itex]?

    An example is easy enough. What's your favorite continuous f? Your favorite a? Your favorite b larger than a? Just plug them in.

    Say, we use
    f(t) = t²
    a = 3
    b = 7

    Then the mean value theorem says that the equation

    [tex]
    \int_3^7 t^2 \, dt = x^2 (7 - 3)
    [/tex]

    has a solution with [itex]3 \leq x \leq 7[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mean Value Theorem for Integrals
Loading...