Download Calculus one and several variables 10E Salas solutions manual ch17 PDF

TitleCalculus one and several variables 10E Salas solutions manual ch17
File Size1.6 MB
Total Pages52
Document Text Contents
Page 26

Sec17-07-17.eps

Page 52

P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU

JWDD027-17 JWDD027-Salas-v1 December 7, 2006 16:38

REVIEW EXERCISES 917

49. J(u, v) =

∣∣∣∣∣ e
u cos v eu sin v

−eu sin v eu cos v

∣∣∣∣∣ = e2u

50. Ju, v, w) =

∣∣∣∣∣∣∣∣
2u 2w vw

2w 2v uw

2v 2u uv

∣∣∣∣∣∣∣∣
= (vw − u2)(4uw − 4v2)

51. Set x =
v − u

2
, y =

v + u
2

=⇒ u = y − x, v = y + x, 1 ≤ v ≤ 2, J = −1
2

at x = 0, y = u, y = v =⇒ u = v
at y = 0, −x = u, x = v =⇒ u = −v∫∫
Ω

cos
(
y − x
y + x

)
dx dy =

∫ 2
1

∫ v
−v

1
2

cos
(u
v

)
du dv =

∫ 2
i

v sin 1 dv =
3
2

sin 1

52. By the hint, J =

∣∣∣∣∣∣∣∣∣∣∣

cos θ
u

sin θ
u

2r

−r cos θ
u2

−r sin θ
u2

0

−r sin θ
u

r cos θ
u

0

∣∣∣∣∣∣∣∣∣∣∣
= −2r

3

u3

∫∫∫
T

dx dy dz =
∫ 2π

0

∫ 2
1

∫ 2
1

2r3

u3
dr du dθ =

45π
8

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