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April 15th, 2012, 11:01 AM   #1
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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?
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April 15th, 2012, 02:12 PM   #2
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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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