The definite integral and its properties

Objectives:

1. Define the definite integral
2. Evaluate the definite integral
3. List the properties of definite integrals

Introduction

Referring to the post: An approach to calculate the area under curve: the definite integral, we define the area under the curve between x₀ and x₄ by:

This expression represents the integral of the function between  x₀ and x₄. We can replace these values by a and b.We have :

Method to evaluate definite integrals

We are going to use a practical method discovered by Newton to evaluate definite integrals. This method uses antiderivatives for the evaluation of definite integrals.

Theorem

Properties of definite integrals

Examples

Solve the definite integrals:

Solutions

 

Practice. Use antiderivatives to calculate the following definite integrals:

Interested in learning more about definite integrals visit Center for Integral Development