This section discusses the concept of antiderivative and the theorms related to it.

A derivative provides an easy way to find the rate of changes for a function. On the other hand, an antiderivative is a way to find the function of a given derivative.

An antiderivative of a function f is any function F such that F' = f. It is a reverse process of differentiation.

The notation used to refer to antiderivative is the indefinite integral. ∫f(x)dx means the antiderivative of f with respect to x . If F(x) is an antiderivative of f(x), then

     ∫f(x)dx = F + c

in which c is an arbitrary constant.

The table on the left gives various examples of indefinite integrals.

The method to calculate the antiderivative or indefinite integral can be better understand by finding the antiderivative of function f ^'(x) = x² when f(1) = 7/3.

The indefinite integral rules gives that

The antiderivative of the given function f ^'(x) = x² can be expressed as

In order to determine the constant c, substituting f(1) = 7/3 into the above expression.

     f(1) = 1/3 + c = 7/3

Rearranging the above equation gives

     c = 2

Therefore, the solution of this example is

     f(x) = x³/3 + 2