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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 .© BrainMass Inc. brainmass.com March 7, 2023, 5:02 am ad1c9bdddf
(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 , ...
Riemann integrable is evaluated in this solution.