Explore BrainMass

# Integration of a function

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

(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.

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

#### Solution Preview

See attachment

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