,OpenStax Calculus Volume 2 Instructor Answer and Solution Guide
Chapter 1
Integration
1.1. Approximating Areas
Section Exercises
1. State whether the given sums are equal or unequal.
a. and
b. and
c. and
d. and
Answer: a. They are equal; both represent the sum of the first 10 whole numbers. b. They are
equal; both represent the sum of the first 10 whole numbers. c. They are equal by substituting
. d. They are equal; the first sum factors the terms of the second.
In the following exercises, use the rules for sums of powers of integers to compute the sums.
2.
Answer:
3.
Answer:
Suppose that and . In the following exercises, compute the sums.
4.
Answer:
5.
Answer:
,OpenStax Calculus Volume 2 Instructor Answer and Solution Guide
6.
Answer:
7.
Answer:
In the following exercises, use summation properties and formulas to rewrite and evaluate
the sums.
8.
Answer:
9.
Answer:
10.
Answer:
11.
Answer:
, OpenStax Calculus Volume 2 Instructor Answer and Solution Guide
Let denote the left-endpoint sum using n subintervals and let denote the
corresponding right-endpoint sum. In the following exercises, compute the indicated left
and right sums for the given functions on the indicated interval.
12. L4 for on
Answer:
13. R4 for on
Answer:
14. L6 for on
Answer:
15. R6 for on
Answer:
16. R4 for on
Answer:
17. L4 for on
Answer:
18. R4 for on
Answer:
19. L8 for on
Answer:
20. Compute the left and right Riemann sums—L4 and R4, respectively—for
on . Compute their average value and compare it with the area under the graph of
f.
Answer: . The graph of f is a triangle of area 4.
Chapter 1
Integration
1.1. Approximating Areas
Section Exercises
1. State whether the given sums are equal or unequal.
a. and
b. and
c. and
d. and
Answer: a. They are equal; both represent the sum of the first 10 whole numbers. b. They are
equal; both represent the sum of the first 10 whole numbers. c. They are equal by substituting
. d. They are equal; the first sum factors the terms of the second.
In the following exercises, use the rules for sums of powers of integers to compute the sums.
2.
Answer:
3.
Answer:
Suppose that and . In the following exercises, compute the sums.
4.
Answer:
5.
Answer:
,OpenStax Calculus Volume 2 Instructor Answer and Solution Guide
6.
Answer:
7.
Answer:
In the following exercises, use summation properties and formulas to rewrite and evaluate
the sums.
8.
Answer:
9.
Answer:
10.
Answer:
11.
Answer:
, OpenStax Calculus Volume 2 Instructor Answer and Solution Guide
Let denote the left-endpoint sum using n subintervals and let denote the
corresponding right-endpoint sum. In the following exercises, compute the indicated left
and right sums for the given functions on the indicated interval.
12. L4 for on
Answer:
13. R4 for on
Answer:
14. L6 for on
Answer:
15. R6 for on
Answer:
16. R4 for on
Answer:
17. L4 for on
Answer:
18. R4 for on
Answer:
19. L8 for on
Answer:
20. Compute the left and right Riemann sums—L4 and R4, respectively—for
on . Compute their average value and compare it with the area under the graph of
f.
Answer: . The graph of f is a triangle of area 4.
