# Riemann integration

Define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx.

is f integrable on [0,1]?

the first integration is upper sums and the second is lower sums

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Proof:

We consider an arbitrary partition .

Let , .

In each interval , ...

#### Solution Summary

Riemann integration for rational and irrational numbers are examined. This provides an example of working with Riemann integration.

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