97
Chapter 11: Applications of Integration
738. f (x) = (sin
3 
x)(cos x), 0 2
, π
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739. g x x
x
( ) =
+
2
3
1
, [0, 2]
740. y = sinh x cosh x, [0, ln 3]
741. f r
r
( ) = +
( )
5
1
2
, [1, 4]
742–747 Solve the problem using the average value
formula.
742. The linear density of a metal rod measuring
8 meters in length is f x
x
( ) =
+
14
2
kilograms
per meter, where x is measured in meters
from one end of the rod. Find the average
density of the rod.
743. Find all numbers d such that the average
value of f
 
(x) = 2 + 4x – 3x
2
on [0, d] is
equal to 3.
734. A tank that has the shape of a hemisphere
with a radius of 4 feet is full of water. If the
opening to the tank is 1 foot above the top
of the tank, how much work in foot-pounds
is required to empty the tank?
735. An open tank full of water has the shape of a
right circular cone. The tank is 10 feet across
the top and 6 feet high. In foot-pounds, how
much work is done in emptying the tank by
pumping the water over the top edge? Round
to the nearest foot-pound. (Note: Water
weighs 62.5 pounds per cubic foot.)
Average Value of a Function
736–741 Find the average value of the function
on the given interval by using the formula
f
b a
f x dx
a
b
avg = − ∫
1
( ) .
736. f
 
(x) = x
3
, [–1, 2]
737. f
 
(x) = sin x, 0 3
2
, π
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