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.)
$$\begin{array} { l }
\mathbf { F } ( x , y ) = \left( 18 x ^ { 2 } y ^ { 2 } - 5 y \sin x \right) \mathbf { i } + \left( 12 x ^ { 3 } y + 5 \cos x \right) \mathbf { j } \
C : \mathbf { r } ( t ) = ( - 2 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi
\end{array}$$
A) 24
B) 47
C) 0
D) $- 20 \cos ( - 2 )$

Question

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.)
$$\begin{array} { l } 
\mathbf { F } ( x , y ) = \left( 18 x ^ { 2 } y ^ { 2 } - 5 y \sin x \right) \mathbf { i } + \left( 12 x ^ { 3 } y + 5 \cos x \right) \mathbf { j } \
C : \mathbf { r } ( t ) = ( - 2 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi
\end{array}$$
A) 24
B) 47
C) 0
D) $- 20 \cos ( - 2 )$

Quizplus · Accepted Answer

The Answer of 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.)
$$\begin{array} { l } 
\mathbf { F } ( x , y ) = \left( 18 x ^ { 2 } y ^ { 2 } - 5 y \sin x \right) \mathbf { i } + \left( 12 x ^ { 3 } y + 5 \cos x \right) \mathbf { j } \
C : \mathbf { r } ( t ) = ( - 2 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi
\end{array}$$
A) 24
B) 47
C) 0
D) $- 20 \cos ( - 2 )$

Evaluate ∫CF⋅dr\int _ { C } \mathbf { F } \cdot d \mathbf { r }∫C​F⋅dr

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