Calculate the Circulation of the Field F Around the Closed $\mathbf { F } = x ^ { 2 } y ^ { 3 } \mathbf { i } + x ^ { 2 } y ^ { 3 } \mathbf { j } ;$

question 260

Multiple Choice

Calculate the circulation of the field F around the closed curve C.
- $\mathbf { F } = x ^ { 2 } y ^ { 3 } \mathbf { i } + x ^ { 2 } y ^ { 3 } \mathbf { j } ;$ curve $C$ is the counterclockwise path around the rectangle with vertices at $( 0,0 ) , ( 4,0 ) , ( 4,2 )$ , and $( 0,2 )$

• A) \(\frac { 704 } { 3 }\)
• B) 0
• C) \(- \frac { 320 } { 3 }\)
• D) \(- 256\)

---

Definitions:

Stock Purchased

The act of buying shares in a company, representing partial ownership and possibly entitling the shareholder to dividends and voting rights.

Accounting

The systematic process of recording, measuring, and communicating financial information about economic entities.

Investments

Assets purchased with the aim of generating income or appreciating in value over time, such as stocks, bonds, real estate, or other investments.

Equity Method

An accounting technique used to record investments in other companies where the investor holds significant influence but not full control or majority ownership.