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

= | | sin(x)| dx | ||

= | sin(x)dx | ||

= | (- cos(x)|_{0}^{Π}) | ||

= |

We could also have observed that in a previous section we found the area under this function to be 4, which is by definition the product of 2

**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?

= | 100(1.05)^{t}dt | ||

= | |_{0}^{3} | ||

= | (1.05^{3} - 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*).)

dx | |||

= (2)dx | |||

= + sin^{-1}(x)|_{0}^{1} | = |

which is approximately equal to 0.79. Notice that this result depends critically on the interpretation of the word "average". Here we are thinking of average of the

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