Evaluate the Line Integral $\int \sin x \sin y d x - \cos x \cos y d y \text { using the Fundamental }$

question 38

Multiple Choice

Evaluate the line integral $\int \sin x \sin y d x - \cos x \cos y d y \text { using the Fundamental }$ Theorem of Line Integrals, where $C$ is the line segment from $( 0 , - \pi )$ to $\left( \frac { 3 \pi } { 2 } , \frac { \pi } { 2 } \right)$ .

• A) \(- 2\)
• B) \(- 1\)
• C) 2
• D) 1
• E) 0

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Definitions:

Fixed Proportions

A production technology assumption where inputs must be used in constant, unchanging ratios to produce outputs.

Average Cost

The total cost of production divided by the number of units produced, representing the cost per unit of output.

Production Function

An equation that specifies the output that can be produced with different combinations of inputs or factors of production.

Total Cost

The sum of all expenses incurred in the production of goods or services, including fixed and variable costs.