Problem : Find the average value of f (x) = | sin(x)| from x = 0 to 2Π .We compute
|=||| sin(x)| dx|
|=||(- cos(x)|0 Π )|
Problem : Suppose Eleanor invests 100 dollars in an account that is compounded continuously with an annual yield of 5 percent, so that the number of dollars in the account after t years is given by A(t) = 100(1.05)t . What is the average amount of money in her account over the first 3 years?We have
|=||(1.053 - 1)|
or approximately 107.69 dollars.
Problem : What is the average y -coordinate of a point on the upper half of the unit circle centered at the origin? (You may use that dx = (x/2) + (1/2)sin-1(x) .)The upper half of the unit circle centered at the origin is the graph of the function f (x) = on the interval [- 1, 1] . The average value of f on this interval equals
|= (2) dx|
|= + sin-1(x)|0 1||=|
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