Question 6 A vector field is given by F(r) = zi+a+yk, and a paraboloid is given by S = {(x, y, z) € R³ |z=1-a²-y², z [0, 1]}, as shown in Figure 6. Figure 6 i) Compute the parametric line integral W = F(r(t)). d) dt. dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)i + sin(t))+0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with [[ (V x F). ñ ds. M main.
Question 6 A vector field is given by F(r) = zi+a+yk, and a paraboloid is given by S = {(x, y, z) € R³ |z=1-a²-y², z [0, 1]}, as shown in Figure 6. Figure 6 i) Compute the parametric line integral W = F(r(t)). d) dt. dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)i + sin(t))+0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with [[ (V x F). ñ ds. M main.
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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Needed to be solved last part correctly in 30 minutes and get the thumbs up please show neat and clean work
![Question 6
A vector field is given by F(r) = z2+3+ yk, and a paraboloid is given by
S = {(x, y, z) = R³ |z=1-2² - y², z € [0, 1]}, as shown in Figure 6.
1
Figure 6
i) Compute the parametric line integral W = F(r(t)). dt.
dr(t)
dt
C is the counter-clockwise circular boundary of S in the ry-plane, with para-
metric definition
r(t) = cos(t)2 + sin(t)j +0k, t€ [0,2m).
ii) Compute the curl of F; i.e. Vx F.
iii) Confirm your answer for W with
(V x F). ñ ds.
7x
Mar](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d1f3ce4-4054-4b62-a653-883caa68d0b4%2Feffb8935-124c-4b63-9346-4e8eafaa214e%2Fuudccta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 6
A vector field is given by F(r) = z2+3+ yk, and a paraboloid is given by
S = {(x, y, z) = R³ |z=1-2² - y², z € [0, 1]}, as shown in Figure 6.
1
Figure 6
i) Compute the parametric line integral W = F(r(t)). dt.
dr(t)
dt
C is the counter-clockwise circular boundary of S in the ry-plane, with para-
metric definition
r(t) = cos(t)2 + sin(t)j +0k, t€ [0,2m).
ii) Compute the curl of F; i.e. Vx F.
iii) Confirm your answer for W with
(V x F). ñ ds.
7x
Mar
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