Consider the curve $y=x^{2/3}$:
a. Sketch the curve between $x=-1$ and $x=8$. ( I sketched it already)
b. Explain why the formula $$ \int_{-1}^{8}\,\sqrt{1+ \left({\rm d}y \over {\rm d}x\right)^{2}\,}\,\,{\rm d}x $$ cannot be used to find arc length of the curve sketched. because $\displaystyle{{{\rm d}y \over {\rm d}x} = {2 \over 3x^{1/3}}}$. Therefore, is undefined at $x=0$.
c. Find the arc length of the curve. Solve for $x$, $x=y^{3/2}$, and use the arc length with $y$ bounds which are from $1$ to $4$.
