9 FURTHER APPLICATIONS OF INTEGRATION

GROUP WORK 1, SECTION 9.3
TheFloatingCenter
1. Consider the region bounded by y = sec x, x =− 1 2 , x = 1 2 ,andthex-axis.
y
2
y=sec x
_1
0
1
x
Computethecenterofmass,anddrawitonthefigure.(Hint: x = 0 by symmetry. y can be computed by
evaluating a relatively simple integral.)
2. Now consider the region defined by y = sec x, x =− π 2 + ε, x = π 2
− ε, and the x-axis.
y
4
y=sec x
2
¹ _2 _
· 0
· ¹ _2
x
Draw in the centers of mass for ε = 0.25 and for ε = 0.01.
3. Some define the center of mass to be the point where a region will balance. What does your second result
mean physically in light of the above definition?
4. Make a conjecture about lim
ε→0
y. What does this mean, physically?
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