Mathematics: Textbook for Class XII (Part II) – NCERT – 1st Edition

Contents

PART II

Foreword v

Preface vii

7. Integrals 287

7.1 Introduction 288

7.2 Integration as an Inverse Process of Differentiation 288

7.3 Methods of Integration 300

7.4 Integrals of some Particular Functions 307

7.5 Integration by Partial Fractions 316

7.6 Integration by Parts 323

7.7 Definite Integral 331

7.8 Fundamental Theorem of Calculus 334

7.9 Evaluation of Definite Integrals by Substitution 338

7.10 Some Properties of Definite Integrals 341

8. Application of Integrals 359

8.1 Introduction 359

8.2 Area under Simple Curves 359

8.3 Area between Two Curves 366

9. Differential Equations 379

9.1 Introduction 379

9.2 Basic Concepts 379

9.3 General and Particular Solutions of a 383

Differential Equation

9.4 Formation of a Differential Equation whose 385

General Solution is given

9.5 Methods of Solving First order, First Degree 391

Differential Equations

10. Vector Algebra 424

10.1 Introduction 424

10.2 Some Basic Concepts 424

10.3 Types of Vectors 427

10.4 Addition of Vectors 429

10.5 Multiplication of a Vector by a Scalar 432

10.6 Product of Two Vectors 441

11. Three Dimensional Geometry 463

11.1 Introduction 463

11.2 Direction Cosines and Direction Ratios of a Line 463

11.3 Equation of a Line in Space 468

11.4 Angle between Two Lines 471

11.5 Shortest Distance between Two Lines 473

11.6 Plane 479

11.7 Coplanarity of Two Lines 487

11.8 Angle between Two Planes 488

11.9 Distance of a Point from a Plane 490

11.10 Angle between a Line and a Plane 492

12. Linear Programming 504

12.1 Introduction 504

12.2 Linear Programming Problem and its Mathematical Formulation 505

12.3 Different Types of Linear Programming Problems 514

13. Probability 531

13.1 Introduction 531

13.2 Conditional Probability 531

13.3 Multiplication Theorem on Probability 540

13.4 Independent Events 542

13.5 Bayes' Theorem 548

13.6 Random Variables and its Probability Distributions 557

13.7 Bernoulli Trials and Binomial Distribution 572

Answers