Projection to xoy plane

First, find the partial derivative of z to x and y.

Ds = √ [square of partial derivative of z to x+square of partial derivative of z to y ]dxdy

The process is as follows:

Extended data:

The driving force of overall development comes from the demand in practical application. In practice, some unknowns can sometimes be roughly estimated, but with the development of science and technology, it is often necessary to know the exact values. If the area or volume of simple geometry is needed, the known formula can be applied.

For example, the volume of a rectangular swimming pool can be calculated by length x width x height. But if the swimming pool is oval, parabolic or more irregular, it is necessary to calculate the volume by integral. In physics, it is often necessary to know the cumulative effect of one physical quantity (such as displacement) on another physical quantity (such as force), and integration is also needed at this time.

References:

Baidu Encyclopedia-Double Integral