Ebook: Handbook of Integration

In performing mathematical analysis, analytic evaluation of integrals
is often required. Other times, an approximate integration may be more
informative than a representation of the exact answer. (The exact representation
could, for example, be in the form of an infinite series.) Lastly, a
numerical approximation to an integral may be all that is required in some
applications.
This book is therefore divided into five sections:
• Applications of Integration which shows how integration is used in
differential equations, geometry, probability and performing summations;
• Concepts and Definitions which defines several different types of integrals
and operations on them;
• Exact Techniques which indicates several ways in which integrals may
be evaluated exactly;
• Approximate Techniques which indicates several ways in which integrals
may be evaluated approximately; and
• Numerical Techniques which indicates several ways in which integrals
may be evaluated numerically.
This handbook has been designed as a reference book. Many of the
techniques in this book are standard in an advanced course in mathematical
methods. Each technique is accompanied by several current references.