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    Integration of a function

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    (a) let f:[0,1] ---R be the function

    f(x) = { x when x is an element of rational numbers
    {-x when x is not an element of rational numbers

    Prove that f is not integrable on [0,1] but |f| is integrable

    (b) Find the limit as x goes to 0 of
    1/x the integral of e^t^2 dt between the boundaries 0 and x, x being the upper boundary.

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    https://brainmass.com/math/integrals/integration-function-2967

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    Problem:

    (a) let f:[0,1] ---R be the function

    f(x) = { x when x is an element of rational numbers
    {-x when x is not an element of rational numbers

    Prove that f is not integrable on [0,1] but ...

    Solution Summary

    This is a proof of integrability and non-integrability, and how to find the limit of a given function.

    $2.49

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