Double integral is the integral of binary function in space, which is similar to definite integral and is the limit of some form of sum. The essence is to find the volume of a curved top cylinder. Multiple integrals have a wide range of applications, which can be used to calculate the area of curved surface, the center of gravity of plane thin plate and so on. The double integral of plane region can be extended to the integral on the (directed) surface in high-dimensional space, which is called surface integral.

When the integrand function is greater than zero, the double integral is the volume of the cylinder.

When the integrand function is less than zero, the double integral is the negative value of the cylinder volume.

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.

Baidu Encyclopedia-Double Integral