Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 44

Multiple Choice

Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ for the vector field $\mathbf { F }$ and the path $C$ . (Hint: Show that $\mathbf { F }$ is conservative, and pick a simpler path.)
$$\mathbf { F } ( x , y ) = \left( 18 x ^ { 2 } y ^ { 2 } - 5 y \sin x \right) \mathbf { i } + \left( 12 x ^ { 3 } y + 5 \cos x \right) \mathbf { j }$$
$C : \mathbf { r } ( t ) = ( - 2 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi$

• A) 24
• B) 47
• C) 0
• D) \(- 20 \cos ( - 2 )\)

---

Definitions:

Biological Psychologists

Scientists who study the biological underpinnings of thoughts, emotions, and behaviors, focusing on brain structures, chemicals, and processes.

Developmental

Pertaining to the process of growth and change in humans across the lifespan, including physical, cognitive, and social-emotional development.

Cognitive

Pertaining to mental processes such as thinking, knowing, remembering, and problem-solving.

Evolutionary Psychologist

A professional who studies how evolutionary principles help explain the structure and function of the human mind.