## Description

This textbook is meant for students of first course on Integral Calculus and Vector Calculus. The book provides balanced coverage of both theory and practice of concepts. A wide variety of problems and lucid language will help students understand and apply the concepts easily. The step-by-step solutions to solved problems enables clear understanding. A variety of solved and unsolved problems have been incorporated to help students ace university and competitive examinations.

## Table of Content

**Chapter1 Methods of Integration**

1.1 Introduction

1.2 Definite Integrals

1.2.1Standard Integrals

1.3Techniques of Integration

1.3.1Integration by Substitution

1.3.2Integration by Trigonometric Substitution

1.3.3Compound Trigonometric Substitution

1.3.4Integration of Rational (Algebraic)Functions

1.3.5Integration of Irrational Functions

1.3.6 Integration by Parts

1.4 Improper Integrals

1.4.1 Integral with Unbounded Integrands

1.4.2 Comparison Tests for Improper Integrals

**Chapter2 Reduction Formulas**

2.1Reduction Formula e − Introduction

2.2Reduction Formula for In= òeaxxn dx

2.3 Reduction Formula forIn= òxn sin ax dx

2.4 Reduction Formula for In=òxa(log x)n dx

2.5Reduction Formula for In=òsinnxdx

2.6 Reduction Formulae for In =òcosnxdxand the Value of ∫_0^(“p” /2)▒cosnxdx

2.7Reduction Formula for Im,n =òsinmx .cosnxdxand the Value of∫_0^(“p” /2)▒sinmx cosnxdx (m and n are Positive Integers)

2.8Reduction Formula for In=òtannxdx

2.9 Reduction Formula for In = òcotnxdx

2.10 Reduction Formula for In=òsecnxdx

2.11Reduction Formula for In =òcosecnxdx

**Chapter 3 Geometrical Applications of Integration**

3.1Formula for the Standard Area

3.2Formulafor the Standard Volume

3.3Formulafor the Length of an Arc of a Curve

3.4Formula for the Area of Surface of Revolution

**Chapter4 Multiple Integrals **

4.1 Introduction

4.2 Evaluation of Double and Triple Integrals

4.3 Region of Integration

4.4 Change of Order of Integration in a Double Integral

4.5 Line Integral

4.6Surface Integral

4.7 Volume Integral

**Chapter 5 Gamma and Beta Functions**

5.1Definitions

5.2 Recurrence Formula for Gamma Function

5.3Symmetry of Beta Functions

5.4 Trigonometric Form of Beta Function

5.5Relation between Gamma and Beta Functions

**Chapter 6 Vector Calculus**

6.1Introduction

6.2 Vector Differential Operator ∇

6.3 The Divergence of a Vector

6.4Line Integral of Vector Point Functions

6.5 Integral Theorems

## About The Author

**T. Veerarajan** is Dean (Retd.), Department of Mathematics, Velammal College of Engineering and Technology, Madurai, Tamil Nadu. A Gold Medalist from Madras University, he has had a brilliant academic career all through. He has 50 years of teaching experience at undergraduate and postgraduate levels in various established engineering colleges in Tamil Nadu including Anna University, Chennai.

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