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    Riemann integration

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    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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    https://brainmass.com/math/integrals/riemann-integration-rational-irrational-numbers-242706

    Solution Preview

    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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