Evaluate the Surface Integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 119

Short Answer

Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ for the vector field $\mathbf { F } ( x , y , z ) = - x \mathbf { i } - y \mathbf { j } + z ^ { 2 } \mathbf { k }$ where S is part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes z = 1 and z = 2 with upward orientation.

---

Definitions:

Debt-to-equity Ratio

Debt-to-equity Ratio is a financial metric that compares a company’s total liabilities to its shareholder equity.

Return on Equity

An indicator of a company's financial success, showing the amount of profit generated from the investments made by its shareholders.

Net Profit Margin

A financial performance metric that shows the percentage of net income derived from revenue.

Earnings Per Share

A financial metric that represents the portion of a company's profit allocated to each outstanding share of common stock, indicating its profitability.