3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along the curves C₁ and C₂ traced out by the vectors. [t³7+ (4t² − 32)J+th] 저 and ri(t)= F(r). dr r₂(t) = 2tī+ (4t-16)+ t€ [0,2] te [0,2] (b) Show that F(x, y, z) is a conservative vector field. (c) State and apply the theorem that guarantees that the integrals in part (a) give the same value.
3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along the curves C₁ and C₂ traced out by the vectors. [t³7+ (4t² − 32)J+th] 저 and ri(t)= F(r). dr r₂(t) = 2tī+ (4t-16)+ t€ [0,2] te [0,2] (b) Show that F(x, y, z) is a conservative vector field. (c) State and apply the theorem that guarantees that the integrals in part (a) give the same value.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve a and b part completly
![3) Consider
-
F(x, y, z) = − ½ 7+ (3² ₂ 2) 7+ yzk
2
(a) Calculate the line integrals
[F(F)-dr
[F(F). dr
along the curves C₁ and C₂ traced out by the vectors.
and
// [er+
[t³7+
(4t² − 32)J+tk]
r₂(t) = 2tī+ (4t - 16)j + k
ri(t) =
te [0,2]
te [0,2]
(b) Show that F(x, y, z) is a conservative vector field.
(c) State and apply the theorem that guarantees that the integrals in part (a)
1.-1
give the same value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F141041e4-6ae6-4884-ac98-550973cc3504%2F46d41dde-8286-42a9-9fe4-34b62858f938%2Fezwjas_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3) Consider
-
F(x, y, z) = − ½ 7+ (3² ₂ 2) 7+ yzk
2
(a) Calculate the line integrals
[F(F)-dr
[F(F). dr
along the curves C₁ and C₂ traced out by the vectors.
and
// [er+
[t³7+
(4t² − 32)J+tk]
r₂(t) = 2tī+ (4t - 16)j + k
ri(t) =
te [0,2]
te [0,2]
(b) Show that F(x, y, z) is a conservative vector field.
(c) State and apply the theorem that guarantees that the integrals in part (a)
1.-1
give the same value.
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