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can we use rienmann sum to calculate the area that is enclosed between a part of a function and the Ox axes in the interval [a,b) if the function is not defined at b ?
can we use rienmann sum to calculate the area that is enclosed between a part of a function and the Ox axes in the interval [a,b) if the function is not defined at b ?
For that matter neither can a large number or even a countably infinite number of isolated points change the value of an integral.
Crosson said:For example, the function:
f(x) = {0 if x is irrational, 1 if x is rational}
has only countably many discontinuities, but it not reimann integrable