Calculating surface surface area with double integral

Let's take an example of an equation

Into equations,

The normal vector at the point is,

and the vertical unit vector perpendicular to the horizontal plane is,

So, we can find the angle between the tangent plane and the horizontal plane, that is, the angle of two plane normal vectors

Surface element Area,

Project experiment: Calculating the sphere surface area of a radius

First, the surface surface area of the first GUA limit is computed, and the surface equation is

The normal vector at the point is,

，

In order to calculate, we convert the upper form into polar coordinates.

Therefore, the total surface area is

Calculating surface surface area with double integral