An integral is a mathematical concept used to calculate areas, volumes, and their generalizations. It is the continuous analog of a sum and is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve or determining displacement from velocity. Today, integration is used in a wide variety of scientific fields.
An integral can be represented as the area of a region under a curve. The process of computing an integral is called integration, and it helps in finding the anti-derivative of a function. The anti-derivative is also called the integral of the function. There are different types of integrals, including definite and indefinite integrals. A definite integral is used to find the area under a curve between two points, while an indefinite integral represents a class of functions whose derivative is the integrand. The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals.
The concept of an integral can be extended to more general domains of integration, such as curved lines and surfaces inside higher-dimensional spaces. Such integrals are known as line integrals and surface integrals.
