Number
Question
Answer
See the work
1.
(A) Estimate the area under the graph of

from x = 0 to x = 5 using 5 approximating rectangles and right
endpoints.
Estimate =
(B) Repeat part (A) using left endpoints.
Estimate =
(C) Repeat part (A) using midpoints.
Estimate =
A) 70
B) 95
C) 83.75
The work Point Cost: 3
2.
Speedometer readings for a motorcycle at 12-seconds intervals are given in the
table.
t(s) 0 12 24 36 48 60
v (ft/s) 25 27 30 24 30 25

(a) Estimate the distance traveled by the motorcycle during this time period
using the velocities at the beginning of the time intervals.
(b)
Give another estimate using the velocities at the end of the time periods.
A) 1632
B) 1632 The work Point Cost: 1
3.
Estimate the area under the graph of

from x = -1 to x = 3, first using 4 approximating
rectangles and right endpoints, and then improving your estimate
using 8 approximating rectangles and right endpoints.
4 Rectangles =
8 Rectangles =
(B) Repeat part (A) using left endpoints.
4 Rectangles =
8 Rectangles =
(C) Repeat part (A) using midpoints.
4 Rectangles =
8 Rectangles =
A) 4 Rectangles = 84
8 Rectangles = 67
B) 4 Rectangles = 28
8 Rectangles = 39
C) 4 Rectangles = 50
8 Rectangles = 51.5
The work Point Cost: 3
4.
The value of the limit

is equal to the area below the graph
of a function f (x) on an interval [A,B]. Find
f , A, and B.
f (x) =
A = (use A=0)
B =
f (x) =
A = 0
B = 4
The work Point Cost: 1
5.
The value of the limit

is equal to the area below the graph
of a function f (x) on an interval [A,B]. Find
f , A, and B.
f (x) =
A =
B =
f (x) = tan(x/2)
A = 0
B = 0.785
The work Point Cost: 1
6.
Estimate the area under the graph of

f (x) = 4/x

from x = 1 to x = 6 using 5 approximating rectangles and right
endpoints.
Estimate =
(B) Repeat part (A) using left endpoints.
Estimate =
A) 5.8
B) 137/15
The work Point Cost: 3