Applications of the Integral

Problems

Problem : Find the average value of f (x) = | sin(x)| from x = 0 to 2Π .

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?

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) .)

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