[内容简介]This book explores the integral calculus and its plentiful applications in engineering and the physical sciences.& The authors aim to develop a basic understanding of integral calculus combined with scientific problems, and throughout, the book details the numerous applications of calculus as well as presents the topic as a deep, rich, intellectual achievement.& The needed fundamental information is presented in addition to plentiful references, exercises, and examples.& The definition of an integral is motivated by the familiar notion of area.& Although the methods of plane geometry allow& for the areas of polygons to be calculated, they do not provide ways of finding the area of plane regions whose boundaries are curves other than circles.& By means of the integral,& the areas of many such regions can be found. The authors& also use& this definition to calculate volumes and length of curves etc.& Topical coverage includes anti-differentiation; integration of trigonometric functions; integration by substitution; methods of substitution; the definite integral; methods for evaluating definite integrals; differential equations and their solutions; and ordinary differential equations of first order and first degree.

[目次]1 Antiderivative(s) [or Indefinite Integral(s)] 
 2 Integration Using Trigonometric Identities
3a Integration by Substitution: Change of Variable of Integration 43
3b Further Integration by Substitution: Additional Standard Integrals 67
4a Integration by Parts 97
4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side 117
5 Preparation for the Definite Integral: The Concept of Area 139
6a The Fundamental Theorems of Calculus 165
6b The Integral Function D x 1 1 t dt, (x > 0) Identified as ln x or loge x 183
7a Methods for Evaluating Definite Integrals 197
7b Some Important Properties of Definite Integrals 213
8a Applying the Definite Integral to Compute the Area of a Plane Figure 249
8b To Find Length(s) of Arc(s) of Curve(s), the Volume(s) of Solid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s) of Revolution 295
9a Differential Equations: Related Concepts and Terminology 321
9b Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree 361
INDEX 399