- #1

irresistible

- 15

- 0

## Homework Statement

Consider

F(x) = x

^{2}sin(1/x

^{2}) if 0<x[tex]\leq1[/tex]

and = 0 if x[tex]\leq0[/tex]

Show that F'(x) exists for all x [tex]\in[a,b] [/tex]

**but**that

**F'**:[0,1] [tex]\rightarrow1[/tex] is

**not**integrable.

## Homework Equations

So we have to show we do not have F(1)-F(0) = [tex]\int[/tex] F'(x)dx

(integral going from 0 to 1)

## The Attempt at a Solution

I'm having trouble proving this statement.

Where should I start?

To show that F'(x) exists, should I just take the derivative or do I have to go under some long theorems of analysis to PROVE?

Thanks in advance.:shy: