A particle on the x$-$axis has a one$-$dimensional wave function given by:

$($x$)=$

A cos$$

$2$xL

$$for $$

L$4$

$$ x $$

L$4$

$0$elsewhere

where

L $>0.$

$($a$)$

Find the normalization constant A in terms of L$.$ Assume A is a positive, real constant.

A $=$

$($b$)$

If the particle's position is measured, what is the probability of finding it between

x $=0$

and

x $=$

L$8$

$?$