# define integral calculus with examples

Sudheesh Singanamalla
114 Points
13 years ago

Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration.

The symbol of integration is $\int \,$, an elongated S (the S stands for "sum"). The definite integral is written as eg.:

$\int_a^b f(x)\, dx.$

and is read "the integral from a to b of f-of-x with respect to x." The Leibniz notation dx is intended to suggest dividing the area under the curve into an infinite number of rectangles, so that their width Δx becomes the infinitesimally small dx. In a formulation of the calculus based on limits.

eg. integrate x^2 dx from 0 to 2

so in the integral formula

$\int_a^b f(x)\, dx.$

a becomes 0 and b becomes 2

then integral x^2 dx = [ x^3 / 2 ] with limits 0 and 2

applying limits we get

8/2 - 0/2 = 4

so integration of x^2 dx from 0 to 2 gives the value as 4

Hope that helps , please approve !