The basic principle of integral:
The basic theorem of calculus was independently founded by isaac newton and Gottfried Wilhelm Leibniz in17th century. The basic theorem of calculus links differential with integral, so that by finding the original function of a function, its integral in an interval can be calculated conveniently. Integrals and derivatives have become the most basic tools in higher mathematics, and are widely used in natural science and engineering.
Bernhard Riemann gave a strict mathematical definition of integral, which is called "Riemann integral". Riemann's definition uses the concept of limit, imagining a curved trapezoid as the limit of a series of rectangular combinations. Since the19th century, with the integration of various types of functions in various integration fields, a more advanced definition of integration has gradually emerged.
For example, path integral is the integral of multivariate function, and the interval of integral is no longer a line segment (interval), but a curve segment in plane or space; In area integration, curves are replaced by surfaces in three-dimensional space. Integral in differential form is a basic concept in differential geometry.