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!

Fundamental Theorem Question

  1. Nov 29, 2006 #1
    Can someone explain a concept to me? The derivative of an integral ( whose lower limit is a real constant and whose upper limit is the variable x), is the intergrand evaluated at x as per the FTofC. I always thought about this as the limit of the integral as x approached the lower limit becuase by definition of the derivative we take limit as change in x approaches 0. So my question is why the derivate of an integral doesn't give the value of the function at the lower limit.
     
  2. jcsd
  3. Nov 29, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Why did you think this? It is not correct. The limit of
    [tex] \int_c^x f(t)dt[/tex]

    as x tends to c is zero.

    What you shuld be thinkig about is

    [tex]\frac{1}{h} (\int_c^{x+h} f(t)dt - \int_c^x f(t)dt)[/tex]

    as h tends to zero.
     
    Last edited: Nov 29, 2006
  4. Nov 29, 2006 #3
    Yes that makes sense. So becuase the lower limit is fixed the rate of change of the area under the curve to the lower limit is zero, but the rate of change of the area up to the upper limit is changing by a value equal the integrand value evaluated at the upper limit?
     
  5. Nov 29, 2006 #4
    I just saw the second equation you posted. That makes it 100% clear to me. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fundamental Theorem Question
  1. Fundamental Theorem (Replies: 4)

  2. Fundamental Theorem? (Replies: 7)

Loading...