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Definition: An integral of a function "F" is the area under the "curve" between specific intervals. It means in the graphic of the function we select an interval, from point a to point b and the area mark by the function, the lines perpendiculars to the axis on the a and b point and the axis itself. It notation for analysis is a symbol like a S, with the intervals in it is extreme followed by the function and next the variable again the integral is used. Example.

Description: - It describes the area under the function on __a__ selected intervals. - If we have a function on n dimensions the integral of that function will be of n+1 dimensions. - There are some functions Which integrals are direct, by example: 1/x, X^n, etc. There are called "Table integrals"

Classification
There are some types of integrals:

Defined Integral: Is a integral in a limited space from A to B, this mean, is the area under the curve with a defined borders.

Example:

Undefined Integral: Opposite to the defined integrals, this has no limits of integrations. This calculate all the area under the curve, in all its extension, even if it is infinite. Example:

Improper integrals: Is an integral that the value of one or both limits is infinite, or a number when the function is not defined.by example: the function: 1/X is not defined when X=0.

Example:

The Integral and derivate are closely related, that is because, an integral is the opposed operation of the derivate, like the subtraction to the addition. This means, if we got a function F and its derivate is F', when we do the undefined integral of F' we got F again.