what is an integral in calculus

An integral is a mathematical concept used in calculus to calculate areas, volumes, and their generalizations. Integration is one of the two fundamental operations of calculus, the other being differentiation. The integral sign ∫ represents integration, and the symbol dx indicates that the variable of integration is x. The function f(x) is called the integrand, and the points a and b are called the limits (or bounds) of integration, and the integral is said to be over the interval . The process of computing an integral is called integration, and it started as a method to solve problems in mathematics and physics, such as finding the area under a curve or determining displacement from velocity. The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton. The theorem demonstrates a connection between integration and differentiation, and this connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals. In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems.