Name______________________
Math 120
Practice Exam 4
For each of the following, please show all your work. Simplify fully. No negative exponents should
appear in your final answer. Unless stated otherwise, each problem is worth 4 points. Deduction for
work done in pen or for work that is hard to follow:_______(up to 2 points).
Formulas:
1) Given the following table, use right-endpoint values to estimate the total amount of pollutants that
were released during the first 40 days.
Time
Pollutants
(days)
(tons/day)
0
0.30
10
0.40
20
0.45
30
0.50
40
0.60
2) Estimate the area under
between 0 and 4 by using 2 rectangles. Let the height of each
rectangle be determined by the midpoint of the interval.
3) (2 points) Evaluate
4) (2 points) Write in sigma notation:
.
5) Find a formula for the Riemann sum for
over
obtained by dividing the interval
into equal subintervals and using the right-hand endpoints for each subinterval. Then find the
limit as
.
6) (2 points) Write as a definite integral
7) Graph the integrand to evaluate the integral.
where P is a partition of
8) Find
9) Evaluate
10) Evaluate
11) Evaluate
. Once you have an expression in x, do not simplify.
12) Evaluate
13) [Set up only] Find the integral that represents the area enclosed by the curves
and