Chapter 13: Area under a Curve; Definite Integrals
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 anti-derivatives and describe tricks for evaluating integrals, which is what these areas are called.
13.1 Areas: Definition, Names, and Notations
13.2 The Fundamental Theorem of Calculus and Determining Areas
13.3 Tricks of Integration