Contents

• Foreword iii
• Preface v

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 Differential Equation 383
• 9.4 Formation of a Differential Equation whose General Solution is given 385
• 9.5 Methods of Solving First order, First Degree Differential Equations 391

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 588

Supplementary Material 613

Courtesy: ncert.nic.in

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