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

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

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

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