Week+22+Feb+9+-13

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Monday Feb 9
Integration by substitution. media type="custom" key="3114910"

Tuesday Feb 10
More practice with volumes of solids.

Wednesday Feb 11
Final review of integration by substitution, area and volume.

Thursday Feb 12
Test - see Second Semester Review page for a copy of the test.

Friday Feb 13
How would you find the average of a set of an infinite number of numbers? This was the concept at the root of the problem posed to us in class today. More specifically, we were asked to consider the average y (or function) value of a function f on a closed interval [a,b]. To begin with, we took specific examples which seemed easy to handle such as those below:

1. f(x) = sin(x) on the interval [0, 2pi] 2. g(x) = cos(x)+ 1 on the interval [0, 2pi]

3 h(x) = x on the interval [0,4] The next problem was significantly more difficult. We had to look at some software, Calculus in Motion, to help us "guess" and check the average value of a function so we could build some insight into what is truly meant by the phrase,the average value of f on [a,b]. The sketch implied an equality between the area of the rectangle, shown in green, and the area under the curve on the interval E-F. We played with several more examples, improving on our guesses each time, until we were finally able to define what we thought the average value of f was intended to be.