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DSN: mth199-101465-0
MA1002 Calculus
Integral Calculus
Dr John Pulham
Contents
List of Figures
How to use these Notes
Integration
The Integral
Doing Integrals
Some Properties of the Indefinite Integral
*Impossible Integrals
The Definite Integral
Differentiating an Integral
Properties of the Definite Integral
Infinite Limits
Questions 1 (Hints and solutions start on page
.)
Applications of Integration
Integrals and Area
Intervals
Further Properties of the Definite Integral
Questions 2 (Hints and solutions start on page
.)
Another View of the Definite Integral
Further Applications of the Definite Integral
The Length of a Curve
Volumes of Revolution
Area of Surface of Revolution
*Area in polar coordinates
Questions 3 (Hints and solutions start on page
.)
*Numerical Approximation to Definite Integrals
*Estimating the value of
e
Methods of Integration
Introduction
Substitution
Substitution in Definite Integrals
The definite integral
Questions 4 (Hints and solutions start on page
.)
Integration by Parts
*The Gamma Function
Questions 5 (Hints and solutions start on page
.)
Quadratics and Trigonometric Substitutions
Questions 6 (Hints and solutions start on page
.)
Integration of Rational Functions and Partial Fractions
Questions 7 (Hints and solutions start on page
.)
*Further Details
Differential Equations
Introduction
Separable Equations
The Malthus Equation
*The Logistic Equation
Generalities
*Linear First-Order Equations
Questions 8 (Hints and solutions start on page
.)
Appendices
Table of Integrals
Solutions to Exercises
Solutions for Questions 1 (page
).
Solutions for Questions 2 (page
).
Solutions for Questions 3 (page
).
Solutions for Questions 4 (page
).
Solutions for Questions 5 (page
).
Solutions for Questions 6 (page
).
Solutions for Questions 7 (page
).
Solutions for Questions 8 (page
).
About this document ...
Ian Craw 2000-01-20
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