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Stewart_Calc_7ET ch08sec02
MULTIPLE CHOICE
1. Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve
about the x-axis on the interval .
a.
b.
c.
d.
e.
2. Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about
the given axis.
y-axis
a.
b.
c.
d.
e.
3. Find the area of the surface obtained by rotating the curve about the x-axis.
a.
b.
c.
d.
e.
4. Find the area of the surface obtained by rotating the curve about the y-axis.
a.
b.
c.
d.
e.
None of these
285
2
5. Find the area of the surface obtained by rotating the circle about the line .
a.
b.
c.
d.
e.
6. Find the volume obtained when the circle of radius with center ( , 0) is rotated about the y-axis.
a.
b.
c.
d.
e.
7. Find the area of the region under the graph of f on [a, b].
a.
–3
b.
–6
c.
6
d.
3
8. Find the area of the surface obtained by revolving the given curve about the x-axis.
on
a.
b.
32
3
c.
d.
9. Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do
not evaluate the integral.)
y = on [3, 6]
a.
b.
8
c.
8
d.
10. If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the area of the surface obtained by rotating the curve about the -axis.
SHORT ANSWER
1. Find the area of the surface obtained by revolving the given curve about the y-axis.
x = on [0, 2]
2. Find the area of the surface obtained by revolving the graph of y = on [0, 1] about the x-axis.
3. Find the area of the surface obtained by revolving the given curve about the x-axis.
on [0, 1]
