Question

find the length of arc for f(x)=x^2/2-ln (x/4)for 2≤x≤4

Answer 1

Arc length is found by the formula
\[\int\limits_{2}^{4} \sqrt{1+ f \prime(x)}\]

Answer 2

f'(x) = x-4/x... a common factor of (x^2-4)/x.
sqrt(1+[(x^2-4)/x]^2) and integrate from 2 to 4. That busy work is for you.