$$
$$
\[ \cos\gamma = \frac{1}{\sqrt{1+f_x^2(x,y) +f_y^2(x,y)}} \]
The area of surface \[ A = \iint_D \sqrt{1 + f_x^2 + f_y^2}\text{d}\sigma \]
If the surface equation can be expressed by the parameter equation: $$
$$
Find the volume surrounded by two cylindrical surface: \(x^2 + y^2 = R^2, x^2 + z^2 = R^2\)
\[ z = \sqrt{R^2 - x^2} \]
\[ \begin{align} V &= 8\iint_D \sqrt{R^2-x^2}\text{d}x\text{d}y\\ &= 8\int_0^R \sqrt{R^2-x^2}\text{d}x\int_0^{\sqrt{R^2-x^2}}\text{d}y\\ &= \end{align} \]