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

Homework Help: Find derivative using FTC1

  1. Nov 25, 2008 #1
    I need to find the derivative of the function below...

    1. The problem statement, all variables and given/known data

    [itex]G(x) = \int_{x}^{1} cos(\sqrt{t}) dt[/itex]

    2. Relevant equations

    FTC1

    If f is continuous on [a,b], then the function g defined by

    [itex]g(x) = \int_{a}^{x} f(t) dt[/itex] [itex]a \leq x \leq b[/itex]

    is continuous on [a,b] and differentiable on (a,b) and [itex]g'(x) = f(x)[/itex]

    3. The attempt at a solution

    Would it be [itex]-cos(sqrt(t))[/itex]

    Thanks for the time!
     
    Last edited: Nov 25, 2008
  2. jcsd
  3. Nov 25, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    It would be [itex]-cos(\sqrt{x})[/itex], not t.
     
  4. Nov 25, 2008 #3

    lurflurf

    User Avatar
    Homework Helper

    First you might reverse the limits, which reveses the sighn. FTC1 says the derivative of the integral of a function is the function. Differendiation cancels integration.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook