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Homework for Chapter 6.5: Average Value of a Function
For the problems that involve a little bit of numeric computation,
feel free to use Excel or some other similar program.
If you see a shortcut, you may take it, as long as you write down that
you are taking the shortcut.
Drill problems:
1: 4x-x^2 on [0,4]
2: sin 4x on [-pi,pi]
3: cube root of x on [1,8]
4: x^2 * sqrt(1+x^3) on [0,2]
10: sqrt(x) on [0,4]
11: 2 sin(x) - sin(2x) on [0,pi]
(note: part (b) can't be solved by hand--use a graphing calculator)
15: midpoint rule for average value of a data table.
Compare your answer
to the simple average of the y values given.
16: average velocity of a car
Applied problems:
17: average temperature from 9am to 9pm
22: avg. flow velocity
Question A:
Use the Midpoint rule with n=6 to find the average value
of the function f(t) = exp(-cos(t)) on the interval [0,2 pi].
These functions (e to the power of a sine/cos wave) are used in
modeling arrival rates that vary cyclically in time.
Question B:

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