what is integration in calculus

Integration is a fundamental operation of calculus, which is the process of computing an integral. It is the continuous analog of a sum and is used to calculate areas, volumes, and their generalizations. The basic idea of integral calculus is finding the area under a curve. To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum them up. Integration is the reverse process of differentiation, where we reduce the functions into parts. The symbol for "Integral" is a stylish "S". 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. 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 can be exploited to calculate integrals. In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems.