Consider the following vector field ? = 2?(2 + sin^2 ?)?̂ + 2? sin ? cos ? ?̂ + 7??̂ a. Compute the divergence of this vector field. b. Use your result from (a) to compute the surface integral over the quarter-cylinder with a radius of 2 and a height of 5, shown in the figure below.

Consider the following vector field ? = 2?(2 + sin^2 ?)?̂ + 2? sin ? cos ? ?̂ + 7??̂ a. Compute the divergence of this vector field. b. Use your result from (a) to compute the surface integral over the quarter-cylinder with a radius of 2 and a height of 5, shown in the figure below.

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

100%

Consider the following vector field
? = 2?(2 + sin^2 ?)?̂ + 2? sin ? cos ? ?̂ + 7??̂
a. Compute the divergence of this vector field.
b. Use your result from (a) to compute the surface integral over the
quarter-cylinder with a radius of 2 and a height of 5, shown in the figure below.

V =
= 2s(2 + sin² p)ŝ + 2s sin p cos $ $ + 7z2

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