Find the Value of the Line Integral $\int_{c} \mathbf{F} \cdot d \mathbf{r}$

question 76

Multiple Choice

Find the value of the line integral $\int_{c} \mathbf{F} \cdot d \mathbf{r}$ on the closed path consisting of line segments from $( 0,2 )$ to $( 0,0 )$ , from $( 0,0 )$ to $( 2,0 )$ , and then from $( 2,0 )$ to $( 0,2 )$ , where $\mathbf { F } ( x , y ) = 3 y e ^ { 3 x y } \mathbf { i } + 3 x e ^ { 3 x y } \mathbf { j }$ .
(Hint: If $\mathbf { F }$ is conservative, the integration may be easier on an alternate path.)

• A) 99
• B) 12
• C) 36
• D) 30
• E) 0

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