Exercises of Integral Calculus E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics: definite and indefinite integrals improper integrals geometric applications and remarkable theorems of integral calculus. Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Simone Malacrida

Exercises of Integral Calculus

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Exercises of Integral Calculus”

INTRODUCTION

DEFINITE AND INDEFINITE INTEGRALS

IMPROPER INTEGRALS

“Exercises of Integral Calculus”

“Exercises of Integral Calculus”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

definite and indefinite integrals

improper integrals

geometric applications and remarkable theorems of integral calculus.

Initial theoretical hints are also presented to make the performance of the exercises understood.

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – DEFINITE AND INDEFINITE INTEGRALS

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

Exercise 23

Exercise 24

Exercise 25

Exercise 26

Exercise 27

Exercise 28

Exercise 29

Exercise 30

Exercise 31

Exercise 32

Exercise 33

Exercise 34

Exercise 35

Exercise 36

Exercise 37

Exercise 38

Exercise 39

Exercise 40

Exercise 41

Exercise 42

Exercise 43

Exercise 44

Exercise 45

Exercise 46

Exercise 47

Exercise 48

Exercise 49

Exercise 50

Exercise 51

Exercise 52

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II – IMPROPER INTEGRALS

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

INTRODUCTION

INTRODUCTION

In this exercise book some examples of calculations related to definite, indefinite and improper integrals are carried out.

Furthermore, the main theorems used in integral calculus are presented, as well as the remarkable geometric applications of this sector of mathematical analysis.

Integral calculus is a milestone in mathematical analysis: the search for primitives and the convergence of improper integrals have represented not only a major mathematical challenge, but also an elegant solution to many physical and applicative problems.

In order to understand in more detail what is explained in the resolution of the exercises, the theoretical context of reference is recalled at the beginning of each chapter.

What is presented in this workbook is generally addressed during the last year of scientific high schools and, above all, in the first course of mathematical analysis proposed at university level.

I

DEFINITE AND INDEFINITE INTEGRALS

DEFINITE AND INDEFINITE INTEGRALS

Considering a continuous function in a closed and bounded interval [a,b], one can define two points within any partition of the interval given by the lower bound and the upper bound as follows:

The lower and upper integral sums are constructed as follows:

We define the following quantity as an integral sum :

The limit of this integral sum (if it exists finitely) is called the Riemann integral and is indicated as follows: