Stewart_Calc_7ET ch07sec04
MULTIPLE CHOICE
1. Use long division to evaluate the integral.
a.
b.
c.
d.
e.
2. Evaluate the integral.
a.
b.
c.
d.
e.
3. Find the integral.
a.
b.
c.
d.
4. Write the form of the partial fraction decomposition of the rational expression. Do not find
the numerical values of the constants.
a.
b.
c.
d.
5. Find the integral.
a.
b.
c.
d.
6. Find the integral.
a.
b.
c.
d.
7. Find the integral.
a.
b.
c.
d.
8. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
9. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
10. Find the integral.
a.
b.
c.
d.
11. Use long division to evaluate the integral.
The choices are rounded to 3 decimal places.
a.
b.
c.
d.
e.
12. Evaluate the integral.
a.
b.
c.
d.
e.
13. Evaluate the integral.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the volume of the resulting solid if the region under the curve
from to is rotated about the x-axis. Round your answer to four decimal places.
2. Make a substitution to express the integrand as a rational function and then evaluate the
integral.
Round the answer to four decimal places.
SHORT ANSWER
1. Eight milligrams of a dye are injected into a vein leading the an individual’s heart. The
concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is
shown in the accompanying table. Use Simpson’s Rule with and the formula
to estimate the person’s cardiac output, where D is the quantity of dye injected in
milligrams, is the concentration of the dye in the aorta, and R is measured in liters per
minute. Round your answer to one decimal place.
t
0
2
4
6
8
10
12
14
16
18
20
22
24
C(t)
0
0
2.6
5.9
9.7
7.9
4.6
3.5
2.2
0.8
0.2
0.1
0
2. Evaluate the integral.
3. Find the integral.
4. Find the integral.
5. Find the integral.
6. A corporation is building a complex of homes, offices, stores, schools, and churches in a
rural community. As a result of this development, the planners have estimated that the
community’s population (in thousands) t years from now will be given by
.
What will the average population of the community be over the next 10 years?
7. The region under the graph of
on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.