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April 15th, 2012, 11:01 AM  #1 
Senior Member Joined: Sep 2008 Posts: 105 Thanks: 0  Differentiability of Riemann Integrable Functions
Suppose f is Riemann integrable on [a,b] and let Is it possible that F?(x) exists but is not equal to f(x)? Is it possible that F?(x) fails to exist? 
April 15th, 2012, 02:12 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,216 Thanks: 493  Re: Differentiability of Riemann Integrable Functions
F'(x) exists. The only caveat is what happens at points of discontinuity of f(x). There F'(x) is undefined. What you are asking about is the fundamental theorem of calculus. 

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differentiability, functions, integrable, riemann 
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