Let $\vec{F}=\operatorname{grad} f$ , Where $f ( x , y ) = \ln \left( 2 x ^ { 2 } + 3 y ^ { 2 } + 1 \right)$

question 19

Short Answer

Let $\vec{F}=\operatorname{grad} f$ , where $f ( x , y ) = \ln \left( 2 x ^ { 2 } + 3 y ^ { 2 } + 1 \right)$ (a)Evaluate the line integral $\int _ { C } \vec { F } \cdot \overline { d r }$ , where C is the line from (0, 0)to (2, -4).
(b)Do you expect the line integral of $\vec{F}$ along the parabola y = x²-4x, 0 $\le$ x $\le$ 2 to equal to the answer to (a)?

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