# Real Analysis: Riemann Integrability

Please see the attached file for the fully formatted problem.

Let E = { 1/n : n 2 N } . Prove that the function

f(x) =

?

1 x 2 E

0 otherwise

is integrable on [0,1]. What is the value of

R

1

0 f(x)dx?

Since this problem is an analysis problem, please be sure to be rigorous.

It falls under the chapter on Integrability on R , where they define partition,

refinement of a partition, upper and lower Riemann sums, (Riemann)

integrability, and upper and lower integrals in terms of the infimum and

supremum of the respective sums.

1

https://brainmass.com/math/real-analysis/real-analysis-riemann-integrability-9711

#### Solution Summary

A function is proven to be Riemann integrable. The solution is detailed and well presented.

$2.19