Answer
$\dfrac{373}{430}$
Work Step by Step
The formula to calculate the arc length is as follows:
$L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows:
$L=\int_{1/2}^{1} [x^4+\dfrac{1}{4x^4}] dx $
Separate the terms and integrate as follows: $L=[ \dfrac{x^5}{5}+\dfrac{x^{-4+1}}{(-4+1)} ]_{1/2}^{1} \\=\dfrac{31}{60} +\dfrac{7}{12} \\=\dfrac{373}{430}$
