Indefinite integral:

BASIC CONCEPT

Let F(x) be a differentiable function of x such that d/dx[F(x)] = f(x). Then F(x) is called as integral of f(x). Symbolically, it is written as ∫f(x) dx = F(x).

f(x), the function to be integrated, is known as integrand.

F(x) is also called as anti-derivative of f(x).

Constant of Integration:

As the differential coefficient of the constant is zero, we know that

.

Thus, ∫f(x) dx = F(x) + c. This constant c is called as constant of integration and can take any real value instead.

INTEGRATION AS THE INVERSE PROCESS OF DIFFERENTIATION

Basic formulae:

Anti derivatives of some of extinsively used functions are given below.

Standard Formulae:

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