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Unformatted text preview: Name 1. (6) What is the average value of the function g (x) =
Give an exact answer. Hint: geometry? √ Homework 18
Section 5.3 16 − x2 on the interval [−4, 4]? √ 2. (6) Given g (x) = sin(x2 ), use the Fundamental Theorem of Calculus to nd 2π √ π g (x) dx. − 2 3. (8) Suppose f (x) is a continuous function. Let A[a,b] denote the average value of f (x)
on the interval [a, b]. Show that A[0,15] is equal to the average of A[0,5] , A[5,10] , and
A[10,15] . That is, write out the average of A[0,5] , A[5,10] , and A[10,15] and show that it is
the same as A[0,15] . Note that you will need to use a property of denite integrals from
section 5.4. ...
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 Spring '08
 KENNEDY
 Calculus, Geometry, Topology, Derivative, Fundamental Theorem Of Calculus, exact answer

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