Use Stoke's Theorem to Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 30

Multiple Choice

Use Stoke's theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $\mathbf { F } ( x , y , z ) = e ^ { - 7 x } \mathbf { i } + e ^ { 4 y } \mathbf { j } + e ^ { 5 z } \mathbf { k }$ and $C$ is the boundary of the part of the plane $8 x + y + 8 z = 8$ in the first octant. Select the correct answer.

• A) 69
• B) 16
• C) 49
• D) 0
• E) 23

---

Definitions:

Interest Charges

Costs incurred by borrowers for the use of borrowed money, typically expressed as an annual percentage rate.

Long-Term Debt

A financial obligation that is due for repayment in more than one year's time.

ROE

Return on Equity (ROE) is a measure of a corporation's profitability that reveals how much profit a company generates with the money shareholders have invested.

Total Assets Turnover

A financial ratio that measures the efficiency of a company's use of its assets to generate sales revenue.