# Examples of definite integrals

# Definite integral

The **definite integral** is the area under the graph of a function delimited on an interval **[A, B] for the X axis and starting from Y = 0** for that axis. The definite integral is represented by an elongated **S** or integral symbol, a variable a in the lower part of the **S** that represents the lower limit of integration, and by a variable **b** that represents the upper limit of integration.

A function **f (x)** represents the function to be integrated and **dx** is called the differential of **x** that represents the integrand or variable on which the integration will be carried out.

Definite integrals **maintain certain properties** or characteristics such as: the value of the integral from **[A to B]** changes sign if the intervals **[B to A]** are inverted , if the limits of integration are equal, then the value of the Integral is 0. If the integral starts at a midpoint from **A to C and from C to A** , the sum of the results is the same as integrating from A to B. If a function is composed of some addition or subtraction, this can be divided into the sums or subtractions respectively said function and said sum of integrals will have the same value of the integral of the complete function.

## Rules of definite integrals

- Every integral extended to a single point interval, [a, a], is equal to zero.
- When the function f (x) is greater than zero, its integral is positive. If the function is less than zero, its integral is negative.
- The integral of a sum of functions is equal to the sum of its integrals taken separately.
- The integral of the product of a constant and a function is equal to the constant times the integral of the function (that is, you can “take” the constant out of the integral).
- By permuting the limits of an integral, it changes sign.