Evaluate the Line Integral $$\int _ { C } \mathbf { F } \cdot d \mathbf { r } \text {, }$$

question 21

Multiple Choice

Evaluate the line integral
$$\int _ { C } \mathbf { F } \cdot d \mathbf { r } \text {, }$$
where $\mathbf { F } ( x , y ) = ( x - y ) \mathbf { i } + ( x y ) \mathbf { j }$ and $C$ is the arc of the circle $x ^ { 2 } + y ^ { 2 } = 16$ traversed counterclockwise from $( 4,0 )$ to $( 0 , - 4 )$ . Round your answer to two decimal places.

• A) \(54.03\)
• B) \(53.03\)
• C) \(55.03\)
• D) \(51.03\)
• E) \(52.03\)

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Definitions:

Direct Materials

Raw materials that are directly traceable to the manufacturing of a product.

Favorable

A term used in accounting and finance to describe a condition or result that is better than expected or budgeted.

Time Variance

The difference between the expected time to complete a task and the actual time taken.

Direct Labor

The labor costs directly associated with the manufacturing of goods, specifically referring to the work of employees who physically produce the products.