|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.
|since the function is odd!|
William Stein 2006-03-15