Evaluate $\int _ { S } \vec { F } \cdot \vec { d A }$

question 16

Essay

Evaluate $\int _ { S } \vec { F } \cdot \vec { d A }$ , where ${ \vec { F } } = x \vec { i } + 6 y \vec { j }$ and S is the part of the cylinder $x ^ { 2 } + y ^ { 2 } = 4$ with x $\ge$ 0, y $\le$ 0, 0 $\ge$ z $\le$ 2, oriented toward the z-axis.

---

Definitions:

Forget

The inability to retrieve information or memories from one's memory.

Effective Listening

The skill of fully focusing on and understanding the speaker's message, involving both hearing and interpreting the information.

Empathetic Listening

The skill of understanding and sharing the feelings of another person by fully concentrating on their words and emotional expressions.

Clarifying

The process of making a statement or situation less confused and more comprehensible.