I want to find the area of the surface $z=b-ax^2$ where 0≤ x ≤ $\sqrt(b/a)$ , -c ≤y ≤ c.
I have parametrized the surface as $\textbf{r}(x,y)=(x, y, b-ax^2)$. I then use the formula \begin{gather*} \iint |r'_{x} \times r'_{y}| dxdy \end{gather*} to calculate the area of the surface which gives me
\begin{gather*} \iint \sqrt(4a^2x^2+1) dxdy \end{gather*}
I set the limits to be 0≤ x ≤ $\sqrt(b/a)$ , -c ≤y ≤ c and end up with the wrong answer. The answer is supposed to be (c$\sqrt2(b+\sqrt(b/a))$. I think I do something wrong when I set my limits, any help would be appreciated!