?A non-integrable function Consider the function defined on [0, 1] such that f(x) = 1 if
Chapter 14, Problem 334(choose chapter or problem)
A non-integrable function Consider the function defined on [0, 1] such that f(x) = 1 if x is a rational number and f(x) = 0 if x is irrational. This function has an infinite number of discontinuities, and the integral \(\int _0^1\ f(x)\ dx\) does not exist. Show that if you consider only right, left, and midpoint Riemann sums on regular partitions with n subintervals, then they equal 1 for all n.
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