Page 85 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II Sachin Kaushal, Lovely Professional University

Notes Unit 6: Properties of Definite Integral

CONTENTS
Objectives
Introduction

6.1 Properties of the Integral
6.1.1 Integrability on all Subintervals
6.1.2 Additivity of the Integral

6.1.3 Inequalities for Integrals
6.1.4 Linear Combinations
6.1.5 Integration by Parts
6.1.6 Change of Variable
6.1.7 Derivative of the Definite Integral

6.2 Summary
6.3 Keywords
6.4 Review Questions

6.5 Further Readings
Objectives

After studying this unit, you will be able to:
 Understand the concept of properties of definite integral
 Explain the various definite integral properties

Introduction

As we know, integration in basic word is the inverse of differentiation. There are two types of
integrals definite and indefinite integral. Definite integral is where the integration is performed
in a specific interval. Usually the integration is performed between a to b, a is known as lower
limit and b is known as upper limit. For integration of definite integral we integrate the specified
function first then apply the upper and lower limit (we subtract upper limit from lower limit).
There are certain properties of definite integral which are discussed in this unit.
Why do we necessitate to study these properties of the definite integral? These properties will
approach to the fundamental theorem of calculus. This theorem is perhaps one of the most
functional in all of mathematics. It converts the integral from a mathematical inquisitiveness to
a prevailing tool that is accessed in science, engineering, economics and many other areas.

6.1 Properties of the Integral

The fundamental properties of integrals are simply attained for us since the integral is defined
straightforwardly by differentiation. Therefore we can pertain all the rules we know regarding
derivatives to attain analogous facts with reference to integrals.

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