The Definite Integral PDF Download

Author: Grigoriĭ Mikhaĭlovich Fikhtengolʹt︠s︡
Publisher: M.E. Sharpe
ISBN:
Category : Mathematics
Languages : en
Pages : 108

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Author: Matthew Boelkins
Publisher: Createspace Independent Publishing Platform
ISBN: 9781724458322
Category :
Languages : en
Pages : 560

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Book Description
Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Author: Deepak Bhardwaj
Publisher: Firewall Media
ISBN: 9788131802069
Category : Definite integrals
Languages : en
Pages : 556

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Author: Dan Sloughter
Publisher: Orange Grove Texts Plus
ISBN: 9781616100896
Category :
Languages : en
Pages : 0

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Author: George Boros
Publisher: Cambridge University Press
ISBN: 9780521796361
Category : Mathematics
Languages : en
Pages : 326

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Book Description
This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.

Author: Demetrios P. KANOUSSIS
Publisher:
ISBN: 9781728820583
Category :
Languages : en
Pages : 197

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Book Description
In solving various problems in Engineering, Physics and Geometry we have to sum up an infinite number of infinitesimal quantities (summands). This leads to the notion of the Definite Integral which is one of the most important concepts in Mathematics.Archimedes (287-211 BC) the great Greek Mathematician and Engineer of antiquity, using his famous "method of exhaustion" was able to evaluate areas of curvilinear plane figures. This method is considered to be the precursor of the contemporary Integral Calculus, discovered independently by Newton (1642-1726) and Leibniz (1646-1716) in the mid-17th century. Indefinite Integrals are studied in considerable depth and extent in my e book "Integrals, Vol. 1, The Indefinite Integral". In this volume we study the "Definite Integral" which is connected to the Indefinite Integral by the so called "The fundamental Theorem of Integral Calculus, (The Newton-Leibniz Theorem)"This book is applications oriented and has been designed to be an excellent supplementary book for University and College students in all areas of Mathematics, Physics and Engineering.The content of the book is divided into 20 chapters as shown analytically in the Table of Contents.In the first five chapters we consider some examples leading directly to the "heart" of the notion of the Definite Integral and study some fundamental properties of the integrals, i.e. integrating finite sums of functions, integrating inequalities, The Mean Value Theorem of Integral Calculus, etc.In chapter 6 we state and prove the two Fundamental Theorems of Integral Calculus.In chapter 7 we develop methods of evaluating Definite Integrals with the aid of the corresponding Indefinite Integrals or by the powerful method of substitution.In chapter 8 we study the integration of complex functions of real arguments.In chapter 9 we define the mean or average value of a function over some finite interval and derive the fundamental formula for the mean value in terms of a definite integral.Chapters 10 and 11 are devoted to the estimation of sums by definite integrals and the definite integrals of even, odd and periodic functions.In chapter 12 we consider the problem of evaluating areas bounded by plane figures (defined in Cartesian or Polar coordinates or in parametric form) with the aid of Definite Integrals.In chapter 13 we evaluate the length of arcs of curves expressed either in Cartesian or Polar coordinates.In chapter 14 we study the computation of volumes of solids.In chapter 15 we evaluate the area of a surface of revolution.In chapter 16 we study the center of gravity of various plane or solid figures for either a discrete or a continuous mass distribution.In chapter 17 we state and prove the two Theorems of the Pappus of Alexandria and consider various applications.In chapter 18 we consider the numerical (approximate) integration, i.e. the Trapezoidal formula, the Simpson's rule, integration by expanding the integrand into a power series, the Gauss's quadrature, etc.In chapter 19 we study the so called "Improper Integrals" which appear quite naturally in various applications. The "Cauchy Principal Value of an improper integral" is defined and various applications are considered. In chapter 20 we consider applications of the Definite Integral in Physics and Engineering, (work of a variable force, distance and displacement, pressure force, power and energy in electric circuits, etc).The text includes 130 illustrative worked out examples and 260 graded problems to be solved. The examples and the problems are designed to help the students to develop a solid background in the evaluation of Integrals, to broaden their knowledge and sharpen their analytical skills and finally to prepare them to pursue successful studies in more advanced courses in Mathematics.A brief hint or a detailed outline in solving more involved problems is often given.

Author: Ulrich L. Rohde
Publisher: John Wiley & Sons
ISBN: 1118130332
Category : Mathematics
Languages : en
Pages : 371

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Book Description
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving. The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. Next, the authors review numerous methods and applications of integral calculus, including: Mastering and applying the first and second fundamental theorems of calculus to compute definite integrals Defining the natural logarithmic function using calculus Evaluating definite integrals Calculating plane areas bounded by curves Applying basic concepts of differential equations to solve ordinary differential equations With this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.

Author: CK-12 Foundation
Publisher: CK-12 Foundation
ISBN: 1935983016
Category : Mathematics
Languages : en
Pages : 603

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Book Description
CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.

Author: Paul J. Nahin
Publisher: Springer Nature
ISBN: 3030437884
Category : Science
Languages : en
Pages : 542

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Book Description
What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.

Author: M. Thamban Nair
Publisher: Springer Nature
ISBN: 3030886379
Category : Mathematics
Languages : en
Pages : 350

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Book Description
This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.