Please see the attached file !!!!

Thanks a lot!

2. Originally Posted by owenji81
Please see the attached file !!!!

Thanks a lot!
Are those definite or indefinite integrals?

RonL

3. indefinite integrals

4. The problem is we cannot find anti-derivatives on closed intervals, we require that $|x|<.5$ in that case $f(x) = 1 \mbox{ on }-.5 and hence the anti-derivative is $x$ on $(-5,5)$ and a constant everywhere.

So,
$f(x) = \left\{ \begin{array}{c}C_1 \mbox{ for }x<-.5\\ x+C_2 \mbox{ for }-.5.5 \end{array} \right\}$

But $f$ needs to be continous differenciable at $x=\pm .5$ as well. So $C_1 = C_2 - .5$ and $C_3 = C_2+.5$ where $C_2$ is any arbitraty konstant.

5. Originally Posted by owenji81
Please see the attached file !!!!

Thanks a lot!
Well I still don't like it so I will do the following instead:

$
c_K(x) = \int_{-\infty}^x K^2(u) du
$

Then:

$c_K(x) = \left\{ \begin{array}{cc}
0 &\mbox{ for }x<-0.5 \\
x + 0.5& \mbox{ for }-0.5\le x \le 0.5 \\
1& \mbox{ for }x>0.5 \end{array}\right.
$

and if you add an arbitary constant onto this $c_K(x)$ you will still have an anti-derivative of $K(x)$.

If everything has worked out right with the extra arbitary constant this should be the same as the soution given by ImPerfectHacker.

RonL