Let Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 118

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = \frac { x \mathbf { i } + y \mathbf { j } + z \mathbf { k } } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } }$ . Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where C is the curve of intersection of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 2 x$ .

• A) \(1\)
• B)\(- 1\)
• C)\(\sqrt { 2 }\)
• D)\(- \sqrt { 2 }\)
• E)\(\sqrt { 3 }\)
• F)\(- \sqrt { 3 }\)
• G)\(2\)
• H)\(0\)

---

Definitions:

Autonomy

Refers to the capacity to make informed, uncoerced decisions independently.

Shame and Doubt

Phases in early child development theorized by Erik Erikson, where children learn to develop autonomy while also experiencing feelings of shame and doubt about their actions.

Trust

The firm belief in the reliability, truth, ability, or strength of someone or something.

Mistrust

The feeling or belief that someone is not reliable, trustworthy, or credible.