Use Stokes's Theorem to Evaluate $\int _ { C } \mathbf { F } \cdot d r$

question 56

Multiple Choice

Use Stokes's Theorem to evaluate $\int _ { C } \mathbf { F } \cdot d r$ where $\mathbf { F } ( x , y , z ) = y z \mathbf { i } + ( 2 - 3 y ) \mathbf { j } + \left( x ^ { 2 } + y ^ { 2 } \right) \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 400$ and $S$ is the first-octant portion of $x ^ { 2 } + y ^ { 2 } \leq 400$ over $x ^ { 2 } + y ^ { 2 } = 400$ . Use a computer algebra system to verify your result.

• A) \(- \frac { 400 } { 3 }\)
• B) 0
• C) \(- \frac { 8000 } { 3 }\)
• D) \(\frac { 400 } { 3 }\)
• E) \(\frac { 8000 } { 3 }\)

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Definitions:

Real Exchange Rate

A measure that compares the relative price of a basket of goods between two countries, adjusted for currency exchange rates.

Basket Of Goods

A set of products and services, considered a representative sample, used to measure the change in overall price levels over time, such as in the calculation of inflation.

Purchasing-Power Parity

An economic theory that states that the exchange rate between two currencies is equal to the ratio of the currencies' respective purchasing powers.

Inflation

A rise in the general level of prices of goods and services in an economy over a period of time, eroding purchasing power.