Name: 
 

MAT 145 Chapter 5 Test (4.9 and 5.1-5.4)



Free Response
 

 1. 

Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

ot001-1.jpg
 

 2. 

Approximate the area under the curve ot002-1.jpg from 0 to ot002-2.jpg using ten approximating rectangles of equal widths and right endpoints.
 

 3. 

Evaluate the Riemann sum for ot003-1.jpg with four subintervals, taking the sample points to be right endpoints.
 

 4. 

If ot004-1.jpg, find the Riemann sum with ot004-2.jpg correct to 3 decimal places, taking the sample points to be midpoints.
 

 5. 

The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval.

ot005-1.jpg
 

 6. 

If ot006-1.jpg and ot006-2.jpg, find ot006-3.jpg.
 

 7. 

Find the area of the region that lies under the given curve.

ot007-1.jpg

Round the result to the nearest thousandth.
 

 8. 

Evaluate the integral by interpreting it in terms of areas.

ot008-1.jpg
 

 9. 

Express the sum as a single integral in the form

ot009-1.jpg

ot009-2.jpg
 

 10. 

Find the derivative of the function.

ot010-1.jpg
 

 11. 

Evaluate the integral if it exists.

ot011-1.jpg
 

 12. 

Evaluate the integral.

ot012-1.jpg
 

 13. 

The marginal cost of manufacturing x yards of a certain fabric is ot013-1.jpg (in dollars per yard). Find the increase in cost if the production level is raised from 500 yards to 3,000 yards.
 

 14. 

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds.

t (s)
0
0.5
1.0
1.5
2.0
2.5
3.0
v (ft/s)
0
4.5
8.4
12.1
13.2
13.3
13.8
 

 15. 

The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.

Use a left sum with ot015-1.jpg.

ot015-2.jpg
 

 16. 

Evaluate the Riemann sum for ot016-1.jpg with four subintervals, taking the sample points to be right endpoints.
 

 17. 

Evaluate the integral by interpreting it in terms of areas.

ot017-1.jpg
 

 18. 

Find the interval on which the curve ot018-1.jpg is concave downward.
 

 19. 

An animal population is increasing at a rate of ot019-1.jpg per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?
 

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 20. 

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

mc020-1.jpg

Select the correct answer.
a.
mc020-2.jpg
b.
mc020-3.jpg
c.
mc020-4.jpg
d.
mc020-5.jpg
e.
mc020-6.jpg
 



 
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