calc notes lecture 23 - Lecture Section 24 5.1 Assignment...

Lecture Section Objectives Assignment
24 5.1 Antiderivatives and Indefinite Integrals
5.1: 1-19 odd, 23, 25, 33-41 odd,
49-61 odd, 71, 75, 77
Understanding Goals:
1. Understand the definition of antiderivative.
2. Understand how to use integral sign for antiderivatives.
3. Understand how to use basic integration rules to find antiderivatives of functions.
4. Understand how to fine particular solutions of indefinite integrals using initial
conditions.
5. Understand how to use antiderivatives to solve real-life problems.
Question to think about:
We know
f x x ( ) = 2
has derivative
f x x '( ) = 2
. Is
x 2
the only function whose derivative
is 2 x ?
Integration is the “inverse” of differentiation
'( ) ( ) F x dx F x C = +
Differentiation is the “inverse” of integration ( ) ( )
d
f x dx f x
dx
� �
=
� �
°
1

Example 1 : Find
a)
5 dx
x
b)
2 x dx
x
c)
x dx