Math 142 (Section 502) Quiz 3 Solutions Spring 2007 1. y = √ x, 1

Math 142 (Section 502) Quiz 3 Solutions Spring 2007 1. y = √ x, 1

Math 142 (Section 502)
1. y =
√
Quiz 3 Solutions
Spring 2007
x, 1 ≤ x ≤ 4, x-axis
S =
v
u
√ u
2π xt1 +
4
Z
1
=
s
4
Z
2π x +
1
Z
=
17/4
1
√
2 x
!2
dx
1
dx
4
2πu1/2 du
5/4
=
4π 3/2
u
3
17/4
5/4
4π
4π
(5/4)3/2 −
(17/4)3/2
3
3
=
≈ 30.85
2. x =
√
3
y, 1 ≤ y ≤ 8, x-axis
S =
2
Z
2πx
3
q
1 + (3x2 )2 dx
1
=
2
Z
√
2πx3 1 + 9x4 dx
1
=
Z
145
10
=
=
π 1/2
u du
18
π 3/2
u
27
145
10
π
π
(145)3/2 − (10)3/2
27
27
≈ 199.48
3. x = y 3 , 0 ≤ y ≤ 1, y-axis
S =
1
Z
2πy
3
q
2πy
3
q
1 + (3y 2 )2 dy
0
=
1
Z
1 + 9y 4 dy
0
=
10
Z
π 1/2
u du
18
1
=
=
π 3/2
u
27
10
1
π
π
(10)3/2 − (1)3/2
27
27
≈ 3.56
√
4. x = 2 1 − y, −1 ≤ y ≤ 0, y-axis
S =
=
v
u
u
t
−1
2π · 2 1 − y 1 + √
1−y
−1
Z
0
Z
0
q
q
4π 2 − y dy
−1
=
2
Z
−4πu1/2 du
3
=
=
−8π 3/2
u
3
2
3
−8π 3/2 −8π 3/2
(2) −
(3)
3
3
≈ 19.84
!2
dy