The calculation of integral is more flexible and complicated than that of derivative. In order to be practical and convenient, commonly used integral formulas are often compiled into tables, which are called integral tables. When calculating the integral, we can find the result in the integral table according to the type of the integrand function, and sometimes we have to go through simple deformation to find the required result in the table.
Extended data
Bernhard Riemann gave a strict mathematical definition of integral (see "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 [a, b]), but a curve segment on the plane or in space; In area integration, curves are replaced by surfaces in three-dimensional space. Integral in differential form is a basic concept in differential geometry.
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