Let Use the Divergence Theorem to Calculate $\int _ { S } { \vec { F } } \cdot \vec { d A }$

question 45

Short Answer

Let $\vec { F } = \frac { x } { \left( x ^ { 2 } + 2 y ^ { 2 } + 4 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { i } + \frac { y } { \left( x ^ { 2 } + 2 y ^ { 2 } + 4 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { j } + \frac { z } { \left( x ^ { 2 } + 2 y ^ { 2 } + 4 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { k }$ Use the Divergence Theorem to calculate $\int _ { S } { \vec { F } } \cdot \vec { d A }$ where S is the sphere of radius $3$ a centered at the point ( $4$ a, 0, 0).

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Definitions:

NPV Technique

A method used in capital budgeting to evaluate the profitability of an investment or project, by calculating the net present value of all cash flows associated with it.

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