Apply Green's Theorem to Evaluate the Integral $$\oint _ { C } ( 6 y d x + 8 y d y )$$

question 141

Multiple Choice

Apply Green's Theorem to evaluate the integral.
- $$\oint _ { C } ( 6 y d x + 8 y d y )$$
$C$ : The boundary of $0 \leq x \leq \pi , 0 \leq y \leq \sin x$

• A) 4
• B) 2
• C) 0
• D) -4

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Definitions:

Inventories

The stockpiles or amounts of goods being held by a business to fulfil future sales or production needs.

Aggregate Expenditure Line

A graphical representation that shows the total spendings in an economy at various levels of national income, illustrating the relationship between overall spending and the output level at which the economy can be in equilibrium.

Income

Refers to the amount of money received over a specific period of time by an individual or group from various sources like wages, investments, or business operations.

Aggregate Expenditure

the total amount of spending on goods and services in an economy during a specific period, including consumption, investment, government spending, and net exports.