Use Green's Theorem to Evaluate the Integral $\int _ { C } ( y - x ) d x + ( 2 y - y ) d y \text { for the }$

question 50

Multiple Choice

Use Green's Theorem to evaluate the integral $\int _ { C } ( y - x ) d x + ( 2 y - y ) d y \text { for the }$ path $C$ defined as $x = 6 \cos \theta , y = 7 \sin \theta$ .

• A) \(210 \pi\)
• B) \(12 \pi\)
• C) \(21 \pi\)
• D) \(126 \pi\)
• E) \(42 \pi\)

---

Definitions:

Selling Price

The amount of money for which a product or service is sold to the customer.

Contribution Margin

The selling price per unit, minus the variable cost per unit, which helps in determining the profitability of products.

Break-even Chart

A graphical representation that shows the point at which total costs and total revenue are equal, indicating no net loss or gain.

Total Revenue

The total amount of money generated by a business from its sales of goods or services before any expenses are subtracted.