Week 3 Homework:
Wed, Thurs, Mon
7.3 trig substitution – text ex 3, #27
7.4 partial fractions – #21 below, #25
7.7 approximate integration — answers as sums
7.8 improper integrals (first case)
8.2 surface areas (rotation about
x
-axis)
2
Homework notes:
In 7.3, #27 done in-class. This
week’s problems are #3, 12, 24 (added), 27. For 7.4,
just the problems from the Fall 2004 list between
#9 and #38. Problems listed from 7.5 remain on
this week’s syllabus.
For 7.7, see example below; decimal approximations
will not be on exam, answers as explicit sums will be.
7.8 - 5,8,9 and 8.2 - 5, 8, 10, 11 as covered in class toda
Problem 7.4.20:
Evaluate
Z
x
2
(
x
-
3)(
x
+ 2)
2
dx.
Solution:
The method of partial fractions says there are
A, B, C
so
x
2
(
x
-
3)(
x
+ 2)
2
=
A
x
-
3
+
B
x
+ 2
+
C
(
x
+ 2)
2
.
As in previous cases, we first clear denominators,
multiplying both sides by
(
x
-
3)(
x
+ 2)
2
,
so
x
2
=
A
(
x
+ 2)
2
+
B
(
x
-
3)(
x
+ 2) +
C
(
x
-
3)
.
Again as in previous cases, we plug in the distinct real
