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!

Proving the second fundamental theorem of calculus?

  1. Jan 10, 2017 #1
    1. The problem statement, all variables and given/known data
    Show that Dx∫f(u)du = f(x) Where the integral is evaluated from a to x. (Hint: Do Taylor expansion of f(u) around x).

    2. Relevant equations
    None

    3. The attempt at a solution
    I have

    ... = Dx(F(u)+C) = Dx(F(x-a)+C) = dxF(x) - dxF(a) = f(x)-f(a). My problem is that it should be only f(x), not f(x) - f(a). I did a taylor expansion of f(u) around x and I'm not sure how that is supposed to help me...
     
  2. jcsd
  3. Jan 10, 2017 #2
    I know that for an integral F(a) (where a is not a variable) the derivative of the integral would be 0, and that's why it would not be included in the final answer, but I don't know how to show that.
     
  4. Jan 10, 2017 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You are starting with ##\int_a^xf(u)du##, so that is a function of x (or maybe of a and x). It is not a function of u.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proving the second fundamental theorem of calculus?
Loading...