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Domain Differentiation question 
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#1
Dec1012, 07:51 PM

P: 376

if a function f is differentiable of [0,2pi] can I integrate its derivative df on [pi, pi]?



#2
Dec1012, 08:51 PM

P: 784

First of all, df is not the derivative of f, it is the differential of f, ##\frac{df}{dx}## is the derivative of x (assuming f is a function of x).
Second of all, why would you think that it's derivative would have a different domain? 


#3
Dec1112, 08:15 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,338

The function, f(x)= 0 if x< 0 and rational or [itex]x> 2\pi[/itex] and rational, f(x)= 1 if x< 0 and irrational or [itex]x> 2\pi[/itex] and irrational, f(x)= 3 for all other x, is differentiable for all x in [itex][0, 2\pi][/itex] but not differentiable for any other f. Since it does not have a derivative on [itex][\pi, 0][/itex], no, its derivative cannot be integegrated there!



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