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

question 24

Multiple Choice

Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ for the vector field F and the path C. (Hint: Show that F is conservative, and pick a simpler path.) $\mathbf { F } ( x , y ) = \left( 16 x ^ { 3 } y ^ { 2 } - 4 y \sin x \right) \mathbf { i } + \left( 8 x ^ { 4 } y + 4 \cos x \right) \mathbf { j }$ C: $\mathbf { r } ( t ) = ( 3 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi$

• A) \(- 16 \cos ( 3 )\)
• B) 54
• C) 0
• D) 19

---

Definitions:

Questions

Inquiries made to seek information, clarify doubts, or provoke thought about a particular subject or issue.

Email Etiquette

Refers to the code of conduct for writing and sending emails, ensuring clarity, professionalism, and respect.

Concise

Expressing or covering much in few words; brief in form but comprehensive in scope.

Greeting

A polite word or sign of welcome or recognition offered upon meeting or arriving.