CHAPTER 20
20.87
If g(x) = Jo f(t) dt, where / is the function of Problem 20.85, find g'(4).
g'(x) = D^* f(t) dt) = /(*). Hence, g'(4) = /(4) = 3.
Problems 20.88-20.90 refer to the function t(x) whose graph is shown in Fig. 20-7.
By definition, the indicated average value
20.92
Find the volume of the solid generated when the region between the semicircle y = 1 -
y = l is rotated around the x-axis (see Fig. 20-8).
Fig. 20-8
By the disk formula,
by Problem 20.71.)
(The integral
and the line
162
Fig. 20-7
20.88
Find
20.89
Find
is the area
20.90
Find
Note that ,4, = |-1-2=1. So, -y4, + A 2 -A 3 = -2 + 3-l = 0.
20.91
Verify that the average value of a linear function f(x) = ax + b
the function at the midpoint of the interval.
over an interval [x t , x 2 ] is equal to the value of
/(*) dx.
/M dx
A 2 = i-3-2 = 3.
f(x) dx.
f(x)dx=-A 1 = -i 2 -2-2=-2.
f(x) dx.
f(x) dx=—A l + A 2 -A 3 .