Suppose that C is the curve of interesection between the plane z = x and the cylinderx² + y?be the interior of this ellipse, oriented with an upward pointing normal vector. IfF(r, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that:1 (an ellipse), oriented counterclockwise when viewed from above. Let SF. drcurl F· dSS

Given that F(x,y,z)=xi+zj+2yk ….(1) The equation of cylinder and plane is x2+y2=1 and z=x…

Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an ellipse), oriented counterclockwise when viewed from above. Let S be the interior of this ellipse, oriented with an upward pointing normal vector. If F(x, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that F. dr = curl F· dS S

Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an ellipse), oriented counterclockwise when viewed from above. Let S be the interior of this ellipse, oriented with an upward pointing normal vector. If F(x, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that F. dr = curl F· dS S

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

Suppose that C is the curve of interesection between the plane z = x and the cylinder
x² + y?
be the interior of this ellipse, oriented with an upward pointing normal vector. If
F(r, y, z) = xi+ zj+ 2y k, verify Stokes' theorem by showing that
:1 (an ellipse), oriented counterclockwise when viewed from above. Let S
F. dr
curl F· dS
S

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