Answer true or false, giving a reason for your answer.Let $\phi ( x , y ) = \ln ( | x y | )$ so that $\nabla \phi = \frac { 1 } { x } \vec { i } + \frac { 1 } { y } \vec { j }$ .
Then $\int _ { C } \nabla \phi \cdot d \vec { r } = \phi ( 1,1 ) - \phi ( - 1,1 )$ where C is given by the parametrization $x = t , y = 1$ for $- 1 \leq t \leq 1$ .

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The Answer of Answer true or false, giving a reason for your answer.Let $\phi ( x , y ) = \ln ( | x y | )$ so that $\nabla \phi = \frac { 1 } { x } \vec { i } + \frac { 1 } { y } \vec { j }$ .
Then $\int _ { C } \nabla \phi \cdot d \vec { r } = \phi ( 1,1 ) - \phi ( - 1,1 )$ where C is given by the parametrization $x = t , y = 1$ for $- 1 \leq t \leq 1$ .

Answer True or False, Giving a Reason for Your Answer ϕ(x,y)=ln⁡(∣xy∣)\phi ( x , y ) = \ln ( | x y | )ϕ(x,y)=ln(∣xy∣)

Answer True or False, Giving a Reason for Your Answer $\phi ( x , y ) = \ln ( | x y | )$