Quiz Answers: (1) 29, (2)
Exam 1: Wednesday, Feb 1, 7:00pm-7:50pm, here.
Why did we skip from §6.5 to §10.3? Later we'll go back and look at trig functions and complex exponentials; these ideas will fit together more than you might expect. We'll go back to §7.1 on Feb 3. |

In this section we use Riemann sums to extend the familiar notion of an average, which provides yet another physical interpretation of integration.

Recall: Suppose are the amount of rain each day in La Jolla, since you moved here. The average rainful per day is

Observation: If you multiply both sides by in Definition 3.3.1, you see that the average value times the length of the interval is the area, i.e., the average value gives you a rectangle with the same area as the area under your function. In particular, in Figure 3.3.1 the area between the -axis and is exactly the same as the area between the horizontal line of height and the -axis.

William Stein 2006-03-15