# Riemann sums

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Given f(x)=x^3 on [0,1] and the partition P={0,1/8,1/3,2/3,1}, find four different Riemann sums R(f,P).

Show that Chi_Q is discontinuous at every point where Chi_Q is the characteristic function for Q - Rational numbers.

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#### Solution Summary

The expert determines the Riemann sums using the left-endpoint rule.

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