SHOW ALL YOUR WORK ON THESE PAGES! TOTAL SCORE = 100
1.
(30 points)
Figure:
The graph of f(x) .
The graph of a function f(x) is shown in Figure 1.
(a)
Estimate the area under the graph between x=2 and x=7 .
(b)
Estimate
2.
(20 points)
A car is traveling back and forth
along a straight road that runs East-West. We make the
convention that positive velocity means velocity Eastward. During a half
hour, we measure the velocity (in miles per hour) every 6 minutes (6
minutes = 0.1 hour), with
the following results.
Use the data in the table to estimate:
(a)
Where the car is at the end of the half hour with
respect to where it was at the beginning.
Tell us explicitly how you are making the estimate!
(b)
How far the car drove (total mileage) during the
half hour. Tell us explicitly how you are making the estimate!
3.
(30 points)
Find anti-derivatives of the following functions:
(a)
(b)
(c)
4.
(20 points)
Calculate the following definite integrals using the ``Evaluation Theorem.''
You must use the Evaluation Theorem to get credit!