Purchase Solution

# Integration of a function

Not what you're looking for?

(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.

##### Solution Summary

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

##### 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 ...

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.