(1) (i) Use the Divergence Theorem to calculate the surface integral /| F- dS, that is, calculate the flux of F across S where F(x, y, 2) = -xzi – yzî + z²k and S is the ellipsoid +5+- = 1. (ii) Use the Divergence Theorem to evaluate (2x + 2y + z2)dS where S is the sphere a² + y² + 2? = 1.

(1) (i) Use the Divergence Theorem to calculate the surface integral /| F- dS, that is, calculate the flux of F across S where F(x, y, 2) = -xzi – yzî + z²k and S is the ellipsoid +5+- = 1. (ii) Use the Divergence Theorem to evaluate (2x + 2y + z2)dS where S is the sphere a² + y² + 2? = 1.

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

(1) (i) Use the Divergence Theorem to calculate the surface integral /| F- dS, that is,
calculate the flux of F across S where
F(x, y, 2) = -xzi – yzî + z²k
and S is the ellipsoid +5+-
= 1.
(ii) Use the Divergence Theorem to evaluate
(2x + 2y + z2)dS
where S is the sphere a² + y² + 2? = 1.

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