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Find a Function F Such That F=f\mathbf { F } = \nabla f

question 77

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Find a function f such that F=f\mathbf { F } = \nabla f and use it to evaluate CFdr\int _ { C } \mathbf { F } \cdot d \mathbf { r } along the curve C. F(x,y)=e2yi+(1+2xe2y)j;C:r(t)=teti+(1+t)j;0t1\mathbf { F } ( x , y ) = e ^ { 2 y } \mathbf { i } + \left( 1 + 2 x e ^ { 2 y } \right) \mathbf { j } ; C : \mathbf { r } ( t ) = t e ^ { t } \mathbf { i } + ( 1 + t ) \mathbf { j } ; 0 \leq t \leq 1

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