Number 
Question 
Answer 
See the work 
1. 
Consider the solid that lies above the square (in the xyplane)
,
and below the elliptic paraboloid
.
(A) Estimate the volume by dividing R into 4 equal squares and choosing the
sample points to lie in the lower left hand corners.
(B) Estimate the volume by dividing R into 4 equal squares and choosing the
sample points to lie in the upper right hand corners..
(C) What is the average of the two answers from (A) and (B)?

A) 92
B) 60
C) 76

The work 
2. 
Consider the solid that lies above the square (in the xyplane)
,
and below the elliptic paraboloid
.
Estimate the volume by dividing R into 9 equal squares and choosing the
sample points to lie in the midpoints of each square.

80.63 
The work 
3. 
Using geometry, calculate the volume of the solid under
and over the circular disk

56.549 
The work 
4. 
Evaluate the iterated integral

2 
The work 
5. 
valuate the iterated integral

0.01626 
The work 
6. 
Evaluate the integral .

5.344 
The work 
7. 
Find

24482.49 
The work 
8. 
Find

24.307 
The work 
9. 
Find where f(x,y) = x and
.
=

180 
The work 
10. 
Find where f(x,y) = 2 x + 5 and
.
= 
60 
The work 
11. 
Calculate the double integral
where R is the region:
.

384 
The work 
12. 
Calculate the double integral
where R is the region:

0.0469 
The work 
13. 
Consider the solid that lies above the square (in the xyplane)
,
and below the elliptic paraboloid
.
Using iterated integrals, compute the exact value of the volume.

220/3 
The work 
14. 
Calculate the volume under the elliptic paraboloid
and over the rectangle
.

896 
The work 
15. 
Find the average value of over the
rectangle .
Average value = 
271.42 
The work 
16. 
Find the average value of over the
rectangle R with vertices (3,0), (3,1), (3,0), (3,1).
Average value =

12.96 
The work 
17. 
If and
, what is the value of
where D is the square: ?

3 
The work 