# Definite Integral

Given a function, f(x), and an interval [a, b], the **definite integral** is equal to the area bounded by the graph of f(x), the x-axis and the vertical lines x = a and x = b.

The **definite integral** is denoted by** **. Where:

**∫** is the sign of integration.

**a** is the lower limit of integration.

**b** is the upper limit of integration.

**f(x) **is the **integrand**.

**dx** is the differential of **x**, and indicates the variable of the function to be integrated.

## Properties of the Definite Integral

1. The value of the **definite integral changes sign** when **interchanging the limits of integration**.

2. If the integration limits coincide, the **definite integral** is **zero**.

3. If *c* is a point inside the interval [a, b], decompose the **definite integral** as a **sum of two integrals** in the interval [a, c] and [c, b].

4. The **definite integral of a sum** of functions equals the **sum of integrals**

5. The integral of the product of a constant of a function is equal to the constant for the integral of the function.