# Defintion of Integration - Indefinite Integral

A function F(x) is called antiderivation of f(x) when it is: F(x) is also called integral of f(x). The procedure of determining the integral is called integration.

Since the derivation of a constant C is zero, then for a function there are an infinite number of integrals:

# Rules of Integration

General Rules

Integrals of Algebraic Functions

Integrals of Trigonometric Functions

Integrals of Inverse Trigonometric Functions

Integrals of Exponential and Logarithmic Functions

Integrals of Hyperbolic Functions

Integrals of Inverse Hyperbolic Functions

### General Rules  # Multiple Integrals

### Double Integral

A double integral consists of two successive integrations of a function of two variables. We calculate each integration independently of the other. We initially calculate the integration inside the brackets, considering x as constant and then we calculate the resulting function with respect to x. Geometrically the result represents the volume between xy plane and the surface f(x,y) in the three dimensional Cartesian System inside the limits of the integration.