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Let LLL be the length of the curve y=14x2−12lnx\displaystyle{y = \frac{1}{4}{x}^2 - \frac{1}{2} \ln x }y=41x2−21lnx for 4≤x≤8.4 \leq x \leq 8.4≤x≤8. If L=a+12lnb,L = a+\frac{1}{2}\ln{b} ,L=a+21lnb, where aaa and bbb are positive integers, what is the value of a+b?a+b?a+b?
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