March 8
HWK #6 due R 3/15 or F 3/16
7.1: 10, 16, 24, 33, 36, 39
7.2: 10, 14, 18, 24, 32, 34
Spring Break March 17-25
Prelim 2: Thursday March 29
Covers up to and including 7.2.
Integration
If F
′
(x) = f(x) then F is an
antiderivative
of f.
Fact. If F and G are antiderivatives of f then
F-G
is a constant
.
If f(t) is velocity at time t, then F(t) is
position. From velocity we can only
determine position up to a constant F(0).
Indefinite integral
If
'( )
( )
then we write
( )
( )
F
x
f x
f x dx
F x
C
=
=
+
∫
We say F is the
indefinite integral
of f.
This
is just another word for antiderivative.
+C reminds us that one we have one
antiderivative we get all the others by
adding a constant.
Integration Formula 1
1
1
(
1)
when
1
1
I1.
1
1
p
p
p
p
p
d
x
p
x
x
p
x
x dx
C
p
dx p
p
+
+
+
=
=
≠
+
=
−
+
+
+
∫
Problem
1
5
2
3
Find the antideriv
ative of
2
6
7
1
1
p
p
x
x dx
C
x
x
x
p
x
p
+
=
+
≠ −
+
+
+
+
∫
Solution
5
2
5
2
1/2
3
3
6
3
3/2
2
1
Find the antiderivative of
2
I don't wri
1
1
te th
6
7
6
7
2
7
2
3
3
e +C
p
p
x
x
x
x
x
x
x
x
x
x
x dx
C
x
x
p
p
x
+
−
−
+
+
+
=
+
+
+
+
+
=
+
−
+
−
≠
∫

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