MATH 151 Engineering Math I, Spring 2014
JD Kim
Week12 Section 5.2, 5.3, 5.5
Section 5.2 Maximum and Minimum Values
Denition Maximum, Minimum
1. A function f has an Absolute Maximum at c if f (c) f (x) for all x in the
domain of f . A function f has an Ab
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week15 Section 6.4
Section 6.4 The Fundamental Theorem of Calculus
Ex1) Compute the following denite integrals using the graph given.
1-1)
A
0
f (x) dx
1-2)
C
0
f (x) dx
1-3)
B
A
f (x) dx
1-4)
D
0
f (x) dx
1
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week14 Section 6.2, 6.3
Section 6.2 Area
Using Rectangles to Approximate the Area Under a Curve
Let f (x) be a function dened on the interval [a, b]. We wish to approximate
the area bounded by the curve f (x
MATH 151 Engineering Math I, Spring 2014
JD Kim
Week13 Section 5.7, 6.1
Section 5.7 Antiderivatives
Denition Antiderivative
We call F (x) an antiderivative of f (x) if F (x) = f (x).
d 2
(x ) = 2x.
ex) x2 is an antiderivative of 2x, because
dx
Denition
If