Problem : Find the average value of f (x) = | sin(x)| from x = 0 to 2Π.We compute
|=||| sin(x)| dx|
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
|= + sin-1(x)|01||=|