Use the Divergence Theorem to evaluate each of the following:(a) // ((2x + yz)i – 2yj + (z² + x)k) · ndS, where S is the sphere z2 + y? + z2 = 4 withoutward (positive) orientation.(b) || (zzi+ 2yj+ 4e*k) · n dS, where S is the surface of the rectangular solid bounded by(zri-I = 0, y = 0, z = 0, r = 1, y = 2, z = 3 with outward (positive) orientation.

a) Given the field, F=2x+yzi-2yj+z2+xk The surface S is the sphere x2+y2+z2=4 with an outward…

Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) · ndS, where S is the sphere z? + y? + z2 outward (positive) orientation. = 4 with (b) H.e (zzi + 2yj + 4e*k) - n dS, where S is the surface of the rectangular solid bounded by I = 0, y = 0, z = 0, r= 1, y = 2, z = 3 with outward (positive) orientation.

Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) · ndS, where S is the sphere z? + y? + z2 outward (positive) orientation. = 4 with (b) H.e (zzi + 2yj + 4e*k) - n dS, where S is the surface of the rectangular solid bounded by I = 0, y = 0, z = 0, r= 1, y = 2, z = 3 with outward (positive) orientation.

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

Use the Divergence Theorem to evaluate each of the following:
(a) // ((2x + yz)i – 2yj + (z² + x)k) · ndS, where S is the sphere z2 + y? + z2 = 4 with
outward (positive) orientation.
(b) || (zzi+ 2yj+ 4e*k) · n dS, where S is the surface of the rectangular solid bounded by
(zri-
I = 0, y = 0, z = 0, r = 1, y = 2, z = 3 with outward (positive) orientation.

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