Parametrization of a Surface in the x-z plane $z=x^2$

Question

I am attempting to parametrise a surface so that I can do a surface integral.

The bounds for my surface are $$ y=0, \\ x^2 \leq z \leq 2, \\ 0 \leq x \leq \sqrt{2}. $$

I have parametrised this as $\textbf{x}(u,v) = (u,0,v)$ where $0 \leq u \leq \sqrt{2}$ and $u^2 \leq v \leq 2$.

Is this the correct idea?

Thanks.

Answer 1

You can also do so

$$y=0$$ $$0\le z \le 2$$

$$0\le x \le \sqrt{z}$$