Question 6 A vector field is given by F(r) = zî+x+yk, and a paraboloid is given by S = {(x, y, z) ER³ |z=1-x² - y², z = [0, 1]}, as shown in Figure 6. 9 Figure 6 r(t) = cos(t) î+ sin(t)j + ok, i) Compute the parametric line integral W = = $x (x(1)). C is the counter-clockwise circular boundary of S in the xy-plane, with para- metric definition ii) Compute the curl of F; i.e. V × F. y iii) Confirm your answer for W with dr(t) dt t = [0, 2π). 11.00 x (V x F) n ds. dt.
Question 6 A vector field is given by F(r) = zî+x+yk, and a paraboloid is given by S = {(x, y, z) ER³ |z=1-x² - y², z = [0, 1]}, as shown in Figure 6. 9 Figure 6 r(t) = cos(t) î+ sin(t)j + ok, i) Compute the parametric line integral W = = $x (x(1)). C is the counter-clockwise circular boundary of S in the xy-plane, with para- metric definition ii) Compute the curl of F; i.e. V × F. y iii) Confirm your answer for W with dr(t) dt t = [0, 2π). 11.00 x (V x F) n ds. dt.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Question 6
A vector field is given by F(r) = z2+x+yk, and a paraboloid is given by
S = {(x, y, z) ER³ |z=1-x² - y², z = [0, 1]}, as shown in Figure 6.
10
X
0
Figure 6
i) Compute the parametric line integral W = = f F(x(t)).
C is the counter-clockwise circular boundary of S in the xy-plane, with para-
metric definition
r(t) = cos(t) + sin(t))+ 0k, te [0, 2π).
ii) Compute the curl of F; i.e. Vx F.
dr(t)
dt
iii) Confirm your answer for W with
11.0x
(V x F). n ds.
dt.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0567139a-9f93-4ba8-a710-9c19173fc9d7%2F3f08a76c-2cb8-4b0b-93d1-05c8fb5c6af8%2Fnjsqxce_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 6
A vector field is given by F(r) = z2+x+yk, and a paraboloid is given by
S = {(x, y, z) ER³ |z=1-x² - y², z = [0, 1]}, as shown in Figure 6.
10
X
0
Figure 6
i) Compute the parametric line integral W = = f F(x(t)).
C is the counter-clockwise circular boundary of S in the xy-plane, with para-
metric definition
r(t) = cos(t) + sin(t))+ 0k, te [0, 2π).
ii) Compute the curl of F; i.e. Vx F.
dr(t)
dt
iii) Confirm your answer for W with
11.0x
(V x F). n ds.
dt.
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