Consider the Vector Field $\vec { F } = ( A x + B y ) \vec { i } + ( B x + C y ) \vec { j }$

Essay

Consider the vector field $\vec { F } = ( A x + B y ) \vec { i } + ( B x + C y ) \vec { j }$ for certain constants A, B and C.
Find the line integral $\int _ { C _ { 1 } } \vec { F } \cdot d \vec { r }$ , where C₁ is the curve $x = e ^ { t ( t - 2 ) } + 6 t , y = \sin \left( \frac { \pi } { 4 } t \right) , 0 \leq t \leq 2$