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

question 145

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

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

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