Question

find arc length of curves

Answer 1

\[24xy=y^4 +48\] y =2 to y=8

Answer 2

first is this an implicit function?

Answer 3

It is, but you can easily write it as an explicit function \(x(y)\).
\[24xy=y^4+48~~\iff~~x=\frac{y^3}{24}+\frac{2}{y}\]The arc length of the curve is then
\[\int_C\mathrm{d}S=\int_2^8\sqrt{1+x'(y)^2}\,\mathrm{d}y\]

Answer 4

thanks