Chapter 18: Area under a Curve

 

Introduction

We will now study the area of very irregular figures. In particular, if we have a curve defined by some function, we will consider the (signed) area between that function and the x axis, between specified values of x. Area above the axis counts as positive area, and that below the axis counts as negative area.
We will be concerned with the definition, nomenclature and notation for such areas, and with means of evaluating them, both exactly and numerically. We will also relate such areas to antiderivatives.

Topics

18.1 Areas: Definition, Names, and Notations

18.2 The Fundamental Theorem of Calculus and Determining Areas

18.3 Tricks of Integration