Use Stokes' Theorem to Evaluate $\int _ { C } ( 3 z - 2 y ) d x + ( 4 x - 2 y ) d y + ( z + 2 y ) d z$

question 13

Multiple Choice

Use Stokes' Theorem to evaluate $\int _ { C } ( 3 z - 2 y ) d x + ( 4 x - 2 y ) d y + ( z + 2 y ) d z$ where C is the circle $x = 3 \cos t , y = 3 \sin t , z = 2,0 \leq t \leq 2 \pi$ .

• A) \(27 \pi\)
• B)\(99 \pi\)
• C)\(18 \pi\)
• D) \(54 \pi\)
• E) \(- 27 \pi\)
• F)\(- 99 \pi\)
• G)\(- 18 \pi\)
• H)\(- 54 \pi\)

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Definitions:

Complements

Goods that are often consumed together, such that an increase in demand for one leads to an increase in demand for the other.

Substitutes

Goods or services that can replace each other in use or consumption, such that an increase in the price of one leads to an increase in demand for the other.

Marginal Revenue

Marginal revenue is the additional revenue that a firm gains from selling one more unit of a good or service.

Demand Curve

A graph showing the relationship between the price of a good and the quantity demanded by consumers at those prices.