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Consider the vector field F = ( 2 x e y − 3 ) i +...

Consider the vector field F = ( 2 x e y − 3 ) i + ( x 2 e y + 2 y ) j ,

(a) Find all potential functions f such that F = ∇ f .

(b) Use (a) to evaluate ∫ C F ⋅ d r , where C is the curve r ( t ) = 〈 t , t 2 〉 , 1 ≤ t ≤ 2 .

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