Let $L$ be the length of the curve $\displaystyle{y = \frac{1}{4}{x}^2 - \frac{1}{2} \ln x }$ for $4 \leq x \leq 8.$ If $L = a+\frac{1}{2}\ln{b} ,$ where $a$ and $b$ are positive integers, what is the value of $a+b?$

Your answer seems reasonable.
Find out if you're right!