Introduction:

Integration is the inverse process of differentiation.

If

(f(x)) = g(x)

we say that f(x) is an integral of g(x). In other words, f(x) is an integral of g(x) if and only if g(x) is the derivative of f(x). For this reason the integral is called the 'Anti-derivative'.

Notation:

If f(x) is an integral of g(x), we write

ò g(x) dx = f(x)

and read the symbol ò as 'integral' (the ò is an elongated S: the connection will become clear when we apply the integral to find the area under curves). In this notation dx separately does not have a meaning.

This symbol dx conveys that x is the variable of integration; this means that the function g(x) as a function of x, is taken, and we are finding a function f(x) whose derivative (with respect to x) is g(x).

The entire notation ò g(x)dx is read as "the integral of g of x with respect to x".
g(x) is called the integrand.