Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$

question 159

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } ( x , y , z ) = y ^ { 2 } z \mathbf { i } + x z \mathbf { j } + x ^ { 2 } y ^ { 2 } \mathbf { k }$ and S is the part of the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ that lies inside the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ , oriented upward.

---

Definitions:

Sales Compensation Plan

A system designed to reward sales employees with commissions, bonuses, or other incentives based on their performance or sales achievements.

Straight Salary Plan

A compensation plan that permits salespeople to be paid for performing various duties that are not reflected immediately in their sales volume.

Sales Volume

The total quantity of products or services sold by a company within a specific period, often used as a measure of business activity.

CEO Compensation

The payment and benefits package provided to a company's chief executive officer, including salary, bonuses, stock options, and other perks.