# Integral Calculus for JEE Main and Advanced PDF

Download Integral Calculus for JEE Main and Advanced PDF book free online – From Integral Calculus for JEE Main and Advanced PDF: This book is a theory cum practice book that equips aspirants to completely master the topic of Integral Calculus for the JEE and other engineering entrance examinations. The author’s (Vinay Kumar) effort is to provide a single-stop resource on this topic to the aspirant. **Buy from Amazon**

Table of Contents

## Description of Integral Calculus for JEE Main and Advanced PDF

This book is meant for students who aspire to join the Indian Institute of Technologies (IITs) and various other engineering institutes through the JEE Main and Advanced examinations. The content has been devised to cover the syllabi of JEE and other engineering entrance examinations on the topic Integral Calculus. The book will serve as a text book as well as practice problem book for these competitive examinations. Integral Calculus for JEE Main and Advanced PDF

As a tutor with more than thirteen years of teaching this topic in the coaching institutes of Kota, I have realised the need for a comprehensive textbook in this subject. I am grateful to McGraw-Hill Education for providing me an opportunity to translate my years of teaching experience into a comprehensive textbook on this subject. This book will help to develop a deep understanding of Integral Calculus through concise theory and problem solving. The detailed table of contents will enable teachers and students to easily access their topics of interest. Each chapter is divided into several segments. Each segment contains theory with illustrative examples. It is followed by Concept Problems and Practice Problems, which will help students assess the basic concepts. At the end of the theory portion, a collection of Target Problems have been given to develop mastery over the chapter. Integral Calculus for JEE Main and Advanced PDF

The problems for JEE Advanced have been clearly indicated in each chapter. The collection of objective type questions will help in a thorough revision of the chapter. The Review Exercises contain problems of a moderate level while the Target Exercises will assess the students’ ability to solve tougher problems. For teachers, this book could be quite helpful as it provides numerous problems graded by difficulty level which can be given to students as assignments. I am thankful to all teachers who have motivated me and have given their valuable recommendations. I thank my family for their whole-hearted support in writing this book. I specially thank Mr. Devendra Kumar and Mr. S. Suman for their co-operation in bringing this book. Suggestions for improvement are always welcomed and shall be gratefully acknowledged. Integral Calculus for JEE Main and Advanced PDF

### Table of Content

1.1 Introduction 1.1

1.2 Elementary Integrals 1.4

1.3 Integration by Transformation 1.10

1.4 Integration by Substitution 1.16

1.5 Integrals Involving Sine and Cosine 1.27

1.6 Rationalization by Trigonometric Substitution 1.36

1.7 Integrals of the Form 1.40

1.8 Integrals of the Form 1.45

1.9 Integrals of the Form 1.50

1.10 Integration of Trigonometric Functions 1.55

1.11 Integration by Parts 1.65

1.12 Special Integrals 1.73

1.13 Multiple Integration by Parts 1.76

1.14 Integration by Reduction Formulae 1.81

1.15 Integration of Rational Functions Using Partial Fractions 1.88

1.16 Special Methods For Integration of Rational Functions 1.101

1.17 Integration of Irrational Functions 1.106

1.18 Integrals of the Type

dx Integral Calculus for JEE Main and Advanced PDF

P Q 1.112

1.19 Integration of a Binomial Differential 1.118

1.20 Euler’s Substitution 1.120

1.21 Method of Undetermined Coefficients 1.124

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1.22 Non-elementary Integrals 1.127

Target Problems for JEE Advanced 1.130

Things to Remember 1.142

Objective Exercises 1.147

Review Exercises for JEE Advanced 1.160

Target Exercises for JEE Advanced 1.162

Previous Year’s Questions (JEE Advanced) 1.164

Answers 1.166

CHAPTER 2 DEFINITE INTEGRATION 2.1 – 2.204

2.1 Introduction 2.1

2.2 Definite Integral as a Limit of Sum 2.5

2.3 Rules of Definite Integration 2.12

2.4 First Fundamental Theorem of Calculus 2.19

2.5 Second Fundamental Theorem of Calculus 2.27

2.6 Integrability 2.41

2.7 Improper Integral 2.52

2.8 Substitution in Definite Integrals 2.63

2.9 Integration by parts for Definite Integrals 2.72

2.10 Reduction Formula 2.78

2.11 Evaluation of Limit of sum using Newton-leibnitz Formula 2.83

2.12 Leibnitz Rule for Differentiation of Integrals 2.91

2.13 Properties of Definite Integral 2.95

2.14 Additional Properties 2.122

2.15 Estimation of Definite Integrals 2.124

2.16 Determination of Function 2.134

2.17 Wallis’ Formula 2.138

2.18 Limit under the sign of Integral 2.143

2.19 Differentiation under the sign of Integral 2.144

2.20 Integration of Infinite Series 2.148

2.21 Approximation of Definite Integrals 2.151

Target Problems for JEE Advanced 2.154

Things to Remember 2.166

Objective Exercises 2.169

Review Exercises for JEE Advanced 2.180

Target Exercises for JEE Advanced 2.184

Content | ix Integral Calculus for JEE Main and Advanced PDF

Previous Year’s Questions (JEE Advanced) 2.188

Answers 2.194

CHAPTER 3 AREA UNDER THE CURVE 3.1 – 3.86

3.1 Curve Sketching 3.1

3.2 Area of a Curvilinear Trapezoid 3.7

3.3 Area Bounded by a Function which Changes Sign 3.10

3.4 Area of a Region Between two Non-intersecting Graphs 3.13

3.5 Area of a Region Between two intersecting Graphs 3.17

3.6 Area by Horizontal Strips 3.21

3.7 Area of a Region Between Several Graphs 3.26

3.8 Determination of Parameters 3.30

3.9 Shifting of Origin 3.35

3.10 Area Bounded by a Closed Curve 3.37

3.11 Areas of Curves given by Parametric Equations 3.42

3.12 Areas of Curves given by Polar Equations 3.44

3.13 Areas of Regions given by Inequalities 3.46

Target Problems for JEE Advanced 3.51

Things to Remember 3.62

Objective Exercises 3.64

Review Exercises for JEE Advanced 3.74

Target Exercises for JEE Advanced 3.76

Previous Year’s Questions (JEE Advanced) 3.78

Answers 3.80

CHAPTER 4 DIFFERENTIAL EQUATIONS 4.1 – 4.99

4.1 Introduction 4.1

4.2 Formation of a Differential Equation 4.3

4.3 Solution of a Differential Equation 4.7

4.4 First Order and First Degree Differential Equations 4.11

4.5 Reducible to Variable Separable 4.17

4.6 Homogeneous Differential Equations 4.23

4.7 Linear Differential Equations 4.30

4.8 Solution by Inspection 4.38

4.9 First Order Higher Degree Differential Equation 4.42

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4.10 Higher Order Differential Equation 4.46

4.11 Integral Equation 4.50

4.12 Problems in Trajectories 4.53

4.13 Applications of Differential Equation 4.55

Target Problems for JEE Advanced 4.61

Things to Remember 4.72

Objective Exercises 4.73

Review Exercises for JEE Advanced 4.84

Target Exercises for JEE Advanced 4.86

Previous Year’s Questions (JEE Advanced) 4.89

Answers 4.92

### Biography

An Elsevier Author, Vinay Kumar, MBBS, MD, FRCPath was born in India in 1944. He earned his medical degree in 1967 from Punjab University Medical College in Amritsar. He completed his PhD in experimental pathology and his residency in anatomic pathology and hematology in 1972 at the All India Institute of Medical Sciences, where he was awarded the Khanolkar Prize for outstanding research in pathology. Integral Calculus for JEE Main and Advanced PDF

Introduction to Integral Calculus PDF(Opens in a new browser tab)

Dr. Kumar came to the United States in 1972 to join the faculty at Boston City Hospital and Boston University, and subsequently moved on to the University of Texas Southwestern Medical Center in 1983, where he served as the Vernie A. Stembridge Professor of Pathology, Associate Dean for Medical Education, and Vice Chairman for Educational Affairs. In 2000 he joined the faculty of the University of Chicago’s Pritzker School of Medicine, where he currently serves as the Executive Vice-Dean of Biological Sciences and the Professor and Chairman of the Department of Pathology.

The author or co-author of five pathology textbooks and teaching aids – the best-known of which is Robbins and Cotran Pathologic Basis of Disease – Dr. Kumar has published more than 100 original articles in scientific journals, a dozen book chapters, and nearly 20 review articles. He has lectured throughout the U.S. and Europe, has served on the editorial boards of several journals, including the Journal of Immunology, and recently completed his term as president of the American Society of Investigative Pathology.