# Riemann integrable

Let f_n(x)= (sin(1/x))^n when x does not equal zero and f_n(x)=0 when x = 0 .

a. Show that f_n(x) is Riemann integrable.

b. Calculate lim(as n goes to infinity) integral ( from 0 to 1) f_n(x)dx .

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#### Solution Preview

Proof:

if ;

(a) I claim that is Riemann Integrable on

For any , we note that is continuous on and thus is Riemann integrable on . So we can find a partition on , such that , ...

#### Solution Summary

Riemann integrable is evaluated in this solution.

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