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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-a²-y², z € [0, 1]}, as shown in Figure 6. 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. V x F. iii) Confirm your answer for W with (V x F). ñ ds. Mar.

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-a²-y², z € [0, 1]}, as shown in Figure 6. 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. V x F. iii) Confirm your answer for W with (V x F). ñ ds. Mar.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Needed to be solved I and II parts 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
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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