Integral Calculus for JEE Main and Advanced

308 Pages·2018·29.47 MB·english

by  Amit M Agarwal

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5
With Sessionwise Theory & Exercises
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Amit M. Agarwal arihant
Skills m
Mathematics for ilif
JEE MAIN &
ADVANCED
Integral
Calculus
With Sessionwise Theory & Exercises
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Skills in
Mathematics for
JEE MAIN &
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I 1
ADVANCED
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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
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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
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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
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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.
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