Chapter 5. APPLICATIONS OF INTEGRATION
5.1
AREAS BETWEEN CURVES
5.1.1
AREA BETWEEN TWO CURVES
y = f (x) AND y = g (x)
If f (x) g (x) 0 for x [a, b], then the graph of f lies above
the graph of g , and the region between the two graphs is
b
b
f (x)dx
Area

Chapter 3. APPLICATIONS
OF DIFFERENTIATION
Contents
1. Related Rates
2. Extreme Values
3. The Mean Value Theorem. Shapes of Curves
4. Sketching the Graph of a Function
5. LHpitals Rule
o
6. Optimization Problems
7. Newtons Method
8. Antiderivatives and In

Chapter 4. THE INTEGRAL
4.1
THE AREA PROBLEM
Problem:
Find the area of the region S under the curve y = f (x) over
an interval a x b, where f (x) 0 and f is continuous on
[a, b].
This means that S is bounded by the graph of a continuous
function f , the v

CALCULUS I
Dr. Nguyen Ngoc Hai
DEPARTMENT OF MATHEMATICS
INTERNATIONAL UNIVERSITY, VNU-HCM
March 30, 2010
Dr. Nguyen Ngoc Hai
CALCULUS I
References
Main textbook:
J. Steward, Calculus. Concepts and Contexts, 5th ed., Thomson
Learning, 2001.
Other textbook

THE INTERNATIONAL UNIVERSITY - VIETNAM NATIONAL UNIVERSITY - HCMC
MIDTERM TEST
Date: April . , 2009 Duration: 90 minutes
SUBJECT:
Calculus I
Head of Department of Mathematics
Lecturers
Signature:
N.V. Thu, N. Dinh, J. Harris, N.N. Hai, M.D. Thanh
INSTRUCT

INTERNATIONAL UNIVERSITY
MID-TERM TEST
November 2005
CALCULUS I
(For Classes IT, ET, and BA)
Lecturers: Assoc. Prof., Dr. Nguyen Dinh
Dr. Janet Caroline Harris
Time allowed: 90 minutes
Document prohibited (except dictionaries).
Answer any FOUR of the foll

Questions for case 2
1. What is going on at CPK? What decisions does Susan Collyns face? (10 points)
2. How does debt affect CPK? (80 points)
To answer this question, you have to calculate the variables listed under Exhibit 9 (those
that I have shaded yel