Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fundamental Theorem of Calculus problem

  1. Nov 13, 2008 #1
    1. The problem statement, all variables and given/known data
    The FTC states that
    [tex]{d\over{dx}}\int_a^x f(t)dt = f(x)[/tex]
    Now, how do I do something like
    [tex]{d\over{dx}}\int_a^{g(x)} f(t)dt = ?[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I know that it has to do with the chain rule, but I forgot my textbook at school and I can't seem to find it online (e.g. Wikipedia).
  2. jcsd
  3. Nov 13, 2008 #2


    Staff: Mentor

    Changing the variable to u, where u = g(x), the integral looks like this:
    [tex]{d\over{du}}\int_a^u f(t)dt = f(u)[/tex]

    The trouble is, you want [tex]{d\over{dx}}\int_a^u f(t)dt = f(u)[/tex]

    So if you want d/dx(H(u)), that's the same as d/du(H(u))*du/dx, isn't it? (Here, H(u) represents the value of the definite integral."
  4. Nov 14, 2008 #3
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook