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!

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


    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


    User Avatar
    Science Advisor

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


    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