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Stewart_Calc_7ET ch05sec02
MULTIPLE CHOICE
1. Evaluate the Riemann sum for with four subintervals, taking the
sample points to be right endpoints.
a.
b.
c.
d.
e.
2. If and , find .
a.
b.
c.
d.
e.
3. Evaluate the integral.
Round your answer to the nearest hundredth.
a.
b.
c.
d.
e.
4. Use the Midpoint Rule with n = 5 to approximate the integral.
Round your answer to three decimal places.
a.
b.
c.
d.
e.
5. Use the Midpoint Rule with n = 10 to approximate the integral.
a.
b.
c.
d.
e.
6. Use the given graph of to find the Riemann sum with six subintervals. Take the sample
points to be left endpoints.
a.
8
b.
6
c.
4
d.
3.5
e.
4.5
NUMERIC RESPONSE
1. If , find the Riemann sum with n = 5 correct to 3 decimal places,
taking the sample points to be midpoints.
2. Evaluate by interpreting it in terms of areas.
3. A table of values of an increasing function is shown. Use the table to find an upper
estimate of
.
–45
–37
–27
9
10
23
4. Given that , find .
5. Express the limit as a definite integral on the given interval.
6. Evaluate by interpreting it in terms of areas.
7. Evaluate by interpreting it in terms of areas.
8. Find an expression for the area under the graph of as a limit. Do not evaluate the limit.
9. Find the area of the region that lies under the given curve.
10. Express the integral as a limit of sums. Then evaluate the limit.
