Compute the Flux of the Vector Field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$

question 50

Short Answer

Compute the flux of the vector field $\vec { F } = ( x - 4 y ) \vec { i } + ( 4 y - 2 z ) \vec { j } + 6 x \vec { k }$ through the surface S, where S is the part of the plane z = x + 2y above the rectangle $0 \leq x \leq 2,0 \leq y \leq 3$ oriented upward.
What is the answer if the plane is oriented downward?

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Definitions:

Investment Center

A business segment or unit within an organization for which the manager has control and is responsible for its revenue, expenses, and the assets invested in the center.

Return On Investment

A performance measure used to evaluate the efficiency or profitability of an investment or compare the efficiency of a number of different investments.

Residual Income

The amount of income that exceeds the minimum target return, often used in performance measurement and managerial compensation.

Return On Investment

A performance measure used to evaluate the efficiency or profitability of an investment, calculated by dividing net profit by the cost of the investment.