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.