#4. Evaluate the surface integralF.dSSfor the given vector field F and the oriented surface S. In other words, find the flux of FacrossS.(a) F(x,y,z)=-xi-yj+z°k and S is the part of the cone z =z = 1 and z = 3 with downward orientation.x2 +·y2 between the planes(b) F(x, y,z) = yi – xj + 2zk and S is the hemisphere x2 + y2 + 22 = 4, z > 0, orienteddownward.

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# 4. Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of Facross S. x² + y2 between the planes (a) F(x,y,z)=-xi-yj+z°k and S is the part of the cone z = z = 1 and z = 3 with downward orientation. (b) F(x,y,z) = yi – xj + 2zk and S is the hemisphere x² + y² + z? = 4, z 2 0, oriented downward.

# 4. Evaluate the surface integral F dS for the given vector field F and the oriented surface S. In other words, find the flux of Facross S. x² + y2 between the planes (a) F(x,y,z)=-xi-yj+z°k and S is the part of the cone z = z = 1 and z = 3 with downward orientation. (b) F(x,y,z) = yi – xj + 2zk and S is the hemisphere x² + y² + z? = 4, z 2 0, oriented downward.

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

#4. Evaluate the surface integral
F.dS
S
for the given vector field F and the oriented surface S. In other words, find the flux of Facross
S.
(a) F(x,y,z)=-xi-yj+z°k and S is the part of the cone z =
z = 1 and z = 3 with downward orientation.
x2 +
·y2 between the planes
(b) F(x, y,z) = yi – xj + 2zk and S is the hemisphere x2 + y2 + 22 = 4, z > 0, oriented
downward.

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