1. When asked to sketch the region of $\displaystyle {(x,y)|x^{2}\le y\le 2} $

I'm pretty sure this is just an oval with it's two halves being $\displaystyle x^2 from -\sqrt{2} to \sqrt{2}$ but I'm not sure if thats right.

2. I'm suppose to set up a proper and improper integral to find the length of a curve $\displaystyle y^3 = x from (-1,-1) to (8,2)$.

I believe I've found the proper one to be $\displaystyle \int_{-1}^{2} \sqrt{1+9y^4} dy$

Any hints on what the improper one might be?

Thanks in advance for the help.