93ç-ç‚Bù ‚5

93ç-ç‚Bù ‚5

1. (12 }) ° Z Z

R

sin x²+ 2xy + y²

dx dy, w2 R Ñâ x + y = 1 £sè™WFˇA 5–

2. (12 }) ° Z Z Z

R

e^{(x2+y2+z2)3/2} dx dy dz, w2 R ÑâVÞ z = px²+ y² ¸7 x² + y²+ z² = 1 F¨ˇA5–

3. (14 }) t°£² (positively oriented) À( (simple closed curve) C U) Z

C

(y³−y) dx − x³ dy Ñ|×, 1°w|×M

4. (14 }) ²¾Ò F (x, y, z) = y

1 + x²y², x

1 + x²y² + z

p1 − y²z², y

p1 − y²x² + z

!

(a) t° F 5P?ƒb (potential function)

(b) t°R

CF · dr, w2 C uÊ xy Þí,š-D( r = 1 + cos θ, θ â 0 ƒ π, ¹ C uN²ÑLv‡í²(

5. (12 })S Ñ,,š7Þ x²+ y²+ z² = 1, z ≥ 0, t°

Z Z

S

x²+ y²
z dS

6. (12 }) ²¾Ò F (x, y, z) = (yz⁵,sin (xyz), x), S ÑÓÞ y = 1 − x² −z² rk xz

Þ¬ií¶M, wN²Õx£ y }¾
° Z Z

S

curlF · n dS

7. (12}) q a²+ b²+ c² = 1
I C ÑâÞ ax + by + cz = ⁴₅ ¸7 x²+ y²+ z² = 1 F ó>|(
â°-õ¬ , C 5N²Ñßv‡
°

Z

C

F ·dr, w2 F(x, y, z) = (2y − z)i + (3x + 2z)j + (2x − y)k

8. (12 }) t°

Z Z

S

F ·dS, w2 F (x, y, z) =



xy, −y² 2 , z



, Þ S Ñú_Þ S1, S2, S₃ 5:Õ
w2 S1 Ñ z = 4 − 3x² −3y² / 1 ≤ z ≤ 4, S2 ÑÆ6Þ x² + y² = 1, 0 ≤ z ≤ 1, S3 ÑÞ z = 0

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