MATH 22: Calculus II Exam 2
Spring Semester 2007
Instructions
Attempt all questions. Answers must be justied in order to gain full credit. Calculators are not permitted. Turn this question sheet in with your blue book.
Time allowed: 50 minutes
Some useful
Midterm 2, Math 22, Fall 2008, 11/10/08
Instructions: Write your name and section number. Draw grading table on the cover.
Read each problem carefully and follow all of its instructions. For each of the problems
below, write a clear and concise solution i
Name:_
SID:_
Section:_
Midterm Exam #1-Math 022-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No calculators or notes are permitted. Show
your work. You do not need to simplify your answers.
Problem #1 (10 points)
A 10 meter high monument has
Name:_
SID:_
Section:_
Midterm Exam #3-Math 022-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No calculators or notes are permitted. Show
your work. You do not need to simplify your answers. The following
formula may be of some use:
1 + x 2 d
Math 22 notes
Fundamental Theorem Notes
Class lecture
Basic review online/lecture notes
http:/www.youtube.com/watch?v=C7ducZoLKgw Refer to this later.
The fundamental theorem of calculus is a theorem that links the concept of
the derivative of a function
Math 22 notes
Derivatives Notes
Class lecture
A derivative is a contract between two or more parties whose value is
based on an agreed-upon underlying financial asset, index or security. Common
underlying instruments include: bonds, commodities, currencie
Name:_
SID:_
Section:_
Final Exam -Math 022-F 07
The exam is 3 hours long. No calculators or notes are permitted. Show your
work. You do not need to simplify your answers.
Problem
1
2
3
4
5
6
7
8
Extra Credit
9
Total
Out of 90
Score out
of 10
1
2
1. It is
Final Exam, Math 22, Fall 2008, 12/13/08
Instructions: Write your name and section number. Draw grading table on the cover.
Read each problem carefully and follow all of its instructions. For each of the problems
below, write a clear and concise solution
MATH 22: Calculus II Exam 3 - Practice Problems
Spring Semester 2007
1. A cone with height 12 ft and radius 4 ft, pointing downward, is lled with water to a depth
of 9 ft. Find the work required to pump all the water out over the top. (Water weighs 62.4
l
MATH 22: Calculus II Exam 2 - Practice Problems
Spring Semester 2007
3
1. (i) Calculate the approximations MID(4) and TRAP(4) to
1
(1 x2 ) dx.
(ii) Without evaluating the integral, determine if the approximation is an under-estimate or
an over-estimate.
2
Vikram Rao
Devin Greene
Math 22 Spring 2008
Math 22 Midterm 1 Solutions
1. (25 points)
4
x
2
cos 2 x dx
0
Solution:
This is just normal integration by parts with the formula given by u dv = uv v du . We
shall make the following substitutions:
u = x2
du =
Name:_
SID:_
Section:_
Midterm Exam #2-Math 022-F 07
Instructor: Devin Greene
The exam is 50 minutes long. No calculators or notes are permitted. Show
your work. You do not need to simplify your answers.
Trigonometric Identities
sin 2 x + cos 2 x = 1
1 +
MATH 22: Calculus II Exam 1
Spring Semester 2007
Instructions
Attempt all questions. Answers must be justied in order to gain full credit. Calculators are not permitted. Turn this question sheet in with your blue book.
Time allowed: 50 minutes
Some useful
MATH 22: Calculus II Exam 3
Spring Semester 2007
Instructions
Attempt all questions. Answers must be justied in order to gain full credit. Calculators are not permitted. Turn this question sheet in with your blue book.
Time allowed: 50 minutes
1. (12 poin
Final Exam
Math 22 Spring 2008
Please be sure to include your name at the top of each page that you hand in.
Be concise and clear when writing your solutions. You may use a half sheet of
notebook paper with notes written on both sidees. Good luck!
Name:
P
1. A 10 meter high monument has circular horizontal cross sections each with area A( x ) =
10 exp( x2 /100),where x is the height in meters from the ground. Write out, but do not
evaluate, an integral representing the volume of the monument.
Solution:
10
Midterm Exam
Math 22 Spring 2008
Please be sure to include your name, student identication number, and
discussion section number on the cover page of your blue book.
In the problems that follow, please show all work. Be concise but also clear. Note
that p
Midterm Exam
Math 22 Spring 2008
Please be sure to include your name, student identication number, and discussion
section number on the cover page of your blue book.
This exam consists of indenite and denite integrals. Evaluate them and simplify your answ
SOLUTIONS FOR MATH 22 EXAM 3
1. Express the arclength of the curve y = e x , 0 x 1 as an integral. You do not need to
evaluate the integral.
Solution: The general formula for the arclength of a graph with equation y = f ( x ) with
x-range a x b is given b
Midterm 1, Math 22, Fall 2008, 10/6/08
1) Find the volume of a solid when the region bounded by y = x 2 and y = x revolves
around the x-axis (10 pts)
2) Find the number b so that the average of the function y = bx x 2 on the interval [0,2]
4
(10 pts)
is
3
SOLUTIONS FOR MATH 22 EXAM 2
For Problems #1-#2, evaluate the integral.
1.
e
1
t ln tdt
Solution: Use integration by parts with u = ln t and dv = tdt, so du = (1/t)dt and
v = t2 /2 dt. Using this substitution, we get
e
1
e
t ln tdt =
1
t
t2
dt =
2
4
.
2.
MATH 22 Worksheet 00
Some Reviews
Antiderivatives
1. Find the most general antiderivative of f (x) and check that it is correct by differentiating:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
1
(h) f (x) =
3
x
(i) f (x) = ( x + 1)( x 1)
f (x) = 18x2
f (x) = x3/5
f (x) =