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 $x = e ^ { t ( t - 2 ) } + 6 t , y = \sin \left( \frac { \pi } { 4 } t \right) , 0 \leq t \leq 2$

Question

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

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The Answer of 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 $x = e ^ { t ( t - 2 ) } + 6 t , y = \sin \left( \frac { \pi } { 4 } t \right) , 0 \leq t \leq 2$

Consider the Vector Field F⃗=(Ax+By)i⃗+(Bx+Cy)j⃗\vec { F } = ( A x + B y ) \vec { i } + ( B x + C y ) \vec { j }F=(Ax+By)i+(Bx+Cy)j​

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