Contents
PART II
Foreword
Preface

v
vii

7. Integrals
7.1 Introduction
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals

287
288
288
300
307
316
323
331
334
338
341

8. Application of Integrals
8.1 Introduction
8.2 Area under Simple Curves
8.3 Area between Two Curves

359
359
359
366

9. Differential Equations
9.1 Introduction
9.2 Basic Concepts
9.3 General and Particular Solutions of a
Differential Equation
9.4 Formation of a Differential Equation whose
General Solution is given
9.5 Methods of Solving First order, First Degree
Differential Equations

379
379
379
383

10. Vector Algebra
10.1 Introduction
10.2 Some Basic Concepts
10.3 Types of Vectors
10.4 Addition of Vectors

385
391
424
424
424
427
429

xiv

10.5 Multiplication of a Vector by a Scalar
10.6 Product of Two Vectors

432
441

11. Three Dimensional Geometry
11.1 Introduction
11.2 Direction Cosines and Direction Ratios of a Line
11.3 Equation of a Line in Space
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines
11.6 Plane
11.7 Coplanarity of Two Lines
11.8 Angle between Two Planes
11.9 Distance of a Point from a Plane
11.10 Angle between a Line and a Plane

463
463
463
468
471
473
479
487
488
490
492

12. Linear Programming
12.1 Introduction
12.2 Linear Programming Problem and its Mathematical Formulation
12.3 Different Types of Linear Programming Problems

504
504
505
514

13. Probability
13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes' Theorem
13.6 Random Variables and its Probability Distributions
13.7 Bernoulli Trials and Binomial Distribution

531
531
531
540
542
548
557
572

Answers

588