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Integral Calculus for JEE Main and Advanced PDF

308 Pages·2018·29.47 MB·english
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I 5 With Sessionwise Theory & Exercises Practice ail Objective Questions from - this book on your mobile for FREE Detailed Instructions inside ( O 0 o J Amit M. Agarwal arihant Skills m Mathematics for ilif JEE MAIN & ADVANCED Integral Calculus With Sessionwise Theory & Exercises v a Skills in Mathematics for JEE MAIN & I I 1 ADVANCED f Integral Calculus With Sessionwise Theory & Exercises Amit M. Agarwal sjcarihant ARIHANT PRAKASHAN (Series), MEERUT Skills in Mathematics for Illi JEE MAIN & ADVANCED arihant ARIHANT PRAKASHAN (Series), MEERUT All Rights Reserved * ©AUTHOR No part of this publication may be re-produced, stored in a retrieval system or by any means, lectronic mechanical, photocopying, recording, scanning, web or otherwise without the written permission of the publisher. Arihant has obtained all the information in this book from the sources believed to be reliable and true. However, Arihant or its editors or authors or illustrators don’t take any responsibility for the absolute accuracy of any information published, and the damages or loss suffered thereupon. i All disputes subject to Meerut (UP) jurisdiction only. ADMINISTRATIVE & PRODUCTION OFFICES Regd. Office ‘Ramchhaya’ 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002 Tele: Oil- 47630600,43518550; Fax: Oil- 23280316 Head Office Kalindi, TP Nagar, Meerut (UP) - 250002 Tel: 0121-2401479,2512970,4004199; Fax: 0121-2401648 SALES & SUPPORT OFFICES Agra, Ahmedabad, Bengaluru, Bhubaneswar, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Meerut, Nagpur & Pune * ISBN : 978-93-12146-91-0 Price : ? 255.00 Printed & Bound by Arihant Publications (I) Ltd. (Press Unit) For further information about the books from Arihant, log on to www.arihantbooks.com or email to info@>arihantbooks.com Skills in Mathematics for 10 j JEE MAIN & ADVANCED PREFACE “YOU CAN DO ANYTHING IF YOU SET YOUR MIND TO IT, I TEACH CALCULUS TO JEE ASPIRANTS BUT BELIEVE THE MOST IMPORTANT FORMULA IS COURAGE+ DREAMS = SUCCESS” It is a matter of great pride and honour for me to have received such an overwhelming response to the previous editions of this book from the readers. In a way, this has inspired me to revise this book thoroughly as per the changed pattern of JEE Main & Advanced. I have tried to make the contents more relevant as per the needs of students, many topics have been re-written, a lot of new problems of new types have been added in etcetc. All possible efforts are made to remove all the printing errors that had crept in previous editions. The book is now in such a shape that the students would feel at ease while going through the problems, which will in turn clear their concepts too. A Summary of changes that have been made in Revised & Enlarged Edition • Theory has been completely updated so as to accommodate all the changes made in JEE Syllabus & Pattern in recent years. • The most important point about this new edition is, now the whole text matter of each chapter has been divided into small sessions with exercise in each session. In this way the reader will be able to go through the whole chapter in a systematic way. • Just after completion of theory, Solved Examples of all JEE types have been given, providing the students a complete understanding of all the formats of JEE questions &. the level of difficulty of questions generally asked in JEE. I • Along with exercises given with each session, a complete cumulative exercises have been given at the end of each chapter so as to give the students complete practice for JEE along with the assessment of knowledge that they have gained with the study of the chapter. • Last 10 Years questions asked in JEE Main &Adv, IIT-JEE &. AIEEE have been covered in all the chapters. However I have made the best efforts and put my all calculus teaching experience in revising this book. Still I am looking forward to get the valuable suggestions and criticism from my own fraternity i.e. the fraternity of JEE teachers. I would also like to motivate the students to send their suggestions or the changes that they want to be incorporated in this book. All the suggestions given by you all will be kept in prime focus at the time of next revision of the book. Amit M. Agarwal Skills in Mathematics for Lil J JEE MAIN & ADVANCED CONTENTS 1. INDEFINITE INTEGRAL 1-82 LEARNING PART Session 5 Session 1 • Integration Using Partial Fractions • Fundamental of Indefinite Integral Session 6 Session 2 • Indirect and Derived Substitutions • Methods of Integration Session? / Session 3 • Euler’s Substitution, Reduction Formula and • Some Special Integrals Integration Using Differentiation Session 4 PRACTICE PART • Integration by Parts • • JEE Type Examples • Chapter Exercises 2. DEFINITE INTEGRAL 83-164 LEARNING PART Session 5 Session 1 • Applications of Periodic Functions and • Integration Basics Newton-Leibnitz’s Formula • Geometrical Interpretation of Definite Session 6 Integral • Integration as Limit of a Sum • Evaluation of Definite Integrals by • Applications of Inequality Substitution • Gamma Function Session 2 • Beta Function • Properties of Definite Integral • Wallis Formula Session 3 PRACTICE PART • Applications of Piecewise Function Property • JEE Type Examples Session 4 • Chapter Exercises • Applications of Even-Odd Property and Half the Integral Limit Property Skills in Mathematics for [11 j JEE MAIN & ADVANCED 3. AREA OF BOUNDED REGIONS 165-232 LEARNING PART Session 2 Session 1 • Area Bounded by Two or More Curves • Sketching of Some Common Curves PRACTICE PART • Some More Curves Which Occur Frequently • JEE Type Examples in Mathematics in Standard Forms • Asymptotes • Chapter Exercises • Areas of Curves 4. DIFFERENTIAL EQUATIONS 233-308 LEARNING PART Session 4 Session 1 • Exact Differential Equations • Solution of a Differential Equation Session 5 • Solving of First Order & Higher Degrees Session 2 • Solving of Variable Seperable Form • Application of Differential Equations • Homogeneous Differential Equation • Application of First Order Differential Equations Session 3 • Solving of Linear Differential Equations PRACTICE PART • Bernoulli’s Equation • JEE Type Examples • Orthogonal Trajectory • Chapter Exercises -4 j - 1 Skills in Mathematics for Illi JEE MAIN & ADVANCED .. -J SYLLABUS FOR JEE MAIN Integral Calculus Integral as an anti - derivative. Fundamental integrals involving . algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type dx dx dx dx — > -----> x2 ± a2 x2 ± a2 a 2 - x2 J a2-x 2 dx dx (px + q) dx > ax2 + bx + c ax2+bx + c ax2 + bx + c (px + q)dx 1/7 r‘ ---------— - - 9 a2 ±x2 dx and - a2 dx ax2 + bx + c Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. Differential Equations i Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear ■ differential equations of the type = q(x) ■ Skills in Mathematics for I III 1 JEE MAIN & ADVANCED SYLLABUS FOR JEE ADVANCED Integral Calculus Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, application of the Fundamental Theorem of Integral Calculus. Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations, variables separable method, linear first order differential equations. I I I i

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