Question

Find the exact length of the curve.
x = (y^4/8)+(1/4y^2) 1 ≤ y ≤ 2

Answer 1

see
http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx
or
https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/arc-length

Answer 2

if the problem is
\[ x = \frac{y^4}{8} + \frac{1}{4y^2} \]

first find dx/dy

Answer 3

then evaluate
\[ \int_1^2 \sqrt{1+ \left( \frac{dx}{dy}\right)^2} \ dy \]