Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
242 Chapter 4: Integration
4.3 Riemann Sums and Definite Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the following definite integral by the limit definition.
a.
b.
c.
d.
e.
____ 2. Evaluate the following definite integral by the limit definition.
a. 4375
b.
c. 4372
d. 1125
e.
4.3 Riemann Sums and Definite Integrals 243
____ 3. Evaluate the following definite integral by the limit definition.
a. –216
b. 240
c. –240
d. 192
e. 216
____ 4. Write the following limit as a definite integral on the interval [2 , 5], where ci is any
point in the ith subinterval.
a.
b.
c.
d.
e.
244 Chapter 4: Integration
____ 5. Write the limit , as a definite integral on the interval
where is any point in the subinterval.
a.
b.
c.
d.
e.
____ 6. Write the following limit as a definite integral on the interval where ci is any
point in the subinterval.
a.
b.
c.
4.3 Riemann Sums and Definite Integrals 245
d.
e.
____ 7. Write the limit , as a definite integral on the interval ,
where ci is any point in the subinterval.
a.
b.
c.
d.
e.
246 Chapter 4: Integration
____ 8. The graph of the function is given below. Which of the following
definite integrals yields the area of the shaded region?
a.
b.
c.
d.
e.
4.3 Riemann Sums and Definite Integrals 247
____ 9. The graph of the function is given below. Which of the following definite
integrals yields the area of the shaded region?
a.
b.
c.
d.
e.
248 Chapter 4: Integration
____ 10. Sketch the region whose area is given by the definite integral and then use a
geometric formula to evaluate the integral.
a. 30
b. 15
c. 4
d. 34
e. –17
____ 11. Sketch the region whose area is given by the definite integral and then use a
geometric formula to evaluate the integral.
a. –158
b. 12
c. 80
d. 82
e. –160
____ 12. Sketch the region whose area is given by the definite integral and then use a
geometric formula to evaluate the integral.
a. –1
b. 1
c. 2
d. 4
e. 15
4.3 Riemann Sums and Definite Integrals 249
____ 13. Sketch the region whose area is given by the definite integral and then use a
geometric formula to evaluate the integral.
a.
b.
c.
d.
e.
____ 14. Sketch the region whose area is given by the definite integral and then use a
geometric formula to evaluate the integral.
a.
b.
c.
d.
e.
250 Chapter 4: Integration
____ 15. Evaluate the integral.
given,
a. –156
b. 156
c. 1,016
d. 24
e. 6,630
4.3 Riemann Sums and Definite Integrals 251
____ 16. Evaluate the integral.
given,
a. –180
b. 16
c. –10169
d. –11522
e. –179
252 Chapter 4: Integration
____ 17. Evaluate the integral.
given,
a. –36
b. –146
c. –114
d. 4
e. –58
4.3 Riemann Sums and Definite Integrals 253
____ 18. Evaluate the integral.
given,
a. –65
b. –2377
c. –66
d. –2024
e. –2025
254 Chapter 4: Integration
____ 19. The graph of f consists of line segments, as shown in the figure. Evaluate the definite
integral using geometric formulas.
a. 4
b. 3
c. 1
d. 2
e. 5
4.3 Riemann Sums and Definite Integrals 255
4.3 Riemann Sums and Definite Integrals
Answer Section
