Area and Volume Formulas
In this section we will derive the formulas used to get the area between two curves and the
volume of a solid of revolution.
Area Between Two Curves
We will start with the formula for determining the area between
on the interv
Rates of Change
The purpose of this section is to remind us of one of the more
important applications of derivatives. That is the fact that
represents the rate of change of
. This is an
application that we repeatedly saw in the previous chapter.
The Definition of the Derivative
In the first section of the last chapter we saw that the
computation of the slope of a tangent line, the instantaneous rate
of change of a function, and the instantaneous velocity of an
all required us to compute
In this section were going to introduce a notation that well be
seeing quite a bit in the next chapter. We will also look at an
application of this new notation.
Given a function
we call dy and dx
differentials and the relationship between t