Find a Function F Such That $\mathbf { F } = \nabla f$

question 34

Short Answer

Find a function f such that $\mathbf { F } = \nabla f$ and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve C. $\mathbf { F } ( x , y ) = y \mathbf { i } + ( x + 6 y ) \mathbf { j }$ C is the upper semicircle that starts at (1, 2) and ends at (5, 2).

---

Definitions:

Organizational Design

The process of structuring an organization's strategy, roles, responsibilities, and processes to achieve its goals and objectives effectively.

Analyzability

The extent to which a problem or system can be understood and examined through logical investigation.

Structure Follows Strategy

A principle that organizational structure should be designed to facilitate the strategic objectives the organization seeks to achieve.

Coordination

Coordination is the process of organizing activities and resources efficiently and effectively to ensure that an organization's goals are met.