List of Paper Homework to be Turned In for Math
152.01 (Autumn 2011)
Kiam Heong Kwa
November 8, 2011
Sec 9.1
due 12/01: 2, 4, 8, 12
Sec 8.2
due 11/15: 6, 12, 14, 26, 28, 30
Exercise 30: The upper half of the torus is generated by rotating the curve
(
x

R
)
2
+
y
2
=
r
2
,
y >
0
, about the
y
axis.
Sec 8.1
due 11/15: 4, 6, 10, 14, 16, 20, 34
Exercise 6: The curve consists of two smooth curves of equal length, i.e.,
y
=

b

r
1

x
2
a
2
and
y
=

b

r
1

x
2
a
2
.
Exercise 10: Compare to the solution of exercise 9 in the notes.
Exercise 16:
√
x

x
2
=
p
x
(1

x
)
is deﬁned only for
0
≤
x
≤
1
.
Exercise 20: Based on the coordinates of the points
P
and
Q
, one can assume that
x >
0
.
Sec 7.8
due 11/08: 6, 12, 18, 20, 26, 30, 36, 40, 68
Exercise 26: First use integration by parts
(R
uv
0
dx
=
uv

R
u
0
v dx
)
with
u
= arctan(
x
)
,
v
0
=
x
(1 +
x
2
)
2
. Then use the trigonometric substitution
x
= tan(
θ
)
.
Exercise 40: Use integration by parts