Problem 6Consider the vector field v : R-→ R³ defined byv(r, y, 2) =Let K be the graph of the function g(r, y, 2) = (2 + y)3 over the unit circle, i.e.K = {< x, y, z > |2+ y? < 1, z = (x² + y²)* }0.80.60.40.20.5-0.5-0.0 -0.6 -0.4 -0.2 00.2 04 0.6 0.8The surface K.Calculate the surface integral of the curl of v over K, i.e.curl v · dS.The surface normal of K is thereby assumed to point downwards.

Given vx,y,z=-yxezgx,y,z=x2+y23K=x,y,z x2+y2≤1, z=x2+y23

Problem 6 Consider the vector field v : R → R* defined by v(r, y, 2) = Let K be the graph of the function g(z, y, z) = (r + )³ over the unit circle, i.e. K = {< r, y, z > |r² + y° < 1, z = (r² + y²)*} 0.8 0.6. 0.4 0.2 05 05 -08 00 -04 02 0 02 04 0.6 0.0 The surface K. Calculate the surface integral of the curl of v over K, i.e. curl v · dS. The surface normal of K is thereby assumed to point downwards.

Problem 6 Consider the vector field v : R → R* defined by v(r, y, 2) = Let K be the graph of the function g(z, y, z) = (r + )³ over the unit circle, i.e. K = {< r, y, z > |r² + y° < 1, z = (r² + y²)*} 0.8 0.6. 0.4 0.2 05 05 -08 00 -04 02 0 02 04 0.6 0.0 The surface K. Calculate the surface integral of the curl of v over K, i.e. curl v · dS. The surface normal of K is thereby assumed to point downwards.

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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