# Reimann integrability using analysis

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I want to show that

lim as a goes to 0, of the integral from a to Pi of sin (nx)/ nx dx= integral from 0 to Pi

of f_n(x) dx, where f_n(x) = 1 when x=0 and f_n(x) = sin( nx)/nx when x does not equal zero.

This is equivalent to showing that for |a|<delta, we can find integral from a to Pi of sin (nx)/ nx dx - integral from 0 to Pi of f_n(x) dx|< epsilon

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#### Solution Summary

Reimann integrability using analysis is demonstrated.

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