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Stewart_Calc_7ET ch07sec08
MULTIPLE CHOICE
1. Evaluate the integral or show that it is divergent.
a.
b.
c.
d.
e.
2. Find the area bounded by the curves and between and .
a.
b.
c.
d.
e.
5
4
3. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
a.
Diverges
b.
c.
d.
0
4. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
a.
6
b.
0
c.
3
d.
Diverges
5. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
a.
b.
c.
Diverges
d.
15
−15
2
15
2
6. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
a.
Diverges
b.
0
c.
2
d.
4
7. A manufacturer of light bulbs wants to produce bulbs that last about hours but, of
course, some bulbs burn out faster than others. Let be the fraction of the company's
bulbs that burn out before t hours. lies between 0 and 1.
Let . What is the value of ?
a.
b.
c.
d.
e.
8. The region is represented below.
Find the area of this region to two decimal places.
a.
20.28
b.
c.
d.
e.
9. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
a.
b.
c.
d.
Diverges
10. Evaluate the integral.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
a.
b.
c.
d.
e.
11. Let a and b be real numbers. What integral must appear in place of the question mark ”?” to
make the following statement true?
a.
b.
c.
d.
e.
12. Evaluate the integral.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. For what values of K is the following integral improper?
2. Evaluate the integral if it is convergent.
3. Evaluate the integral or show that it is divergent.
4. Evaluate the integral.
5. Determine whether the integral converges or diverges. If it converges, find its value.
SHORT ANSWER
1. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
2. Determine whether the improper integral converges or diverges, and if it converges, find its
value.
