Let $\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }$

Essay

Let $\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }$ Let $I _ { 1 } = \int _ { C _ { 1 } } \bar { F } \cdot \overline { d r }$ , where C₁ is the line from (0, 0)to (2, 2).
Let $I_{2}=\int_{c_{2}} \vec{F} \cdot \overrightarrow{d r}$ , where C₂ is parameterized by $\vec { r } ( t ) = t \vec { i } + \frac { 1 } { 2 } t ^ { 2 } \vec { j } , \quad 0 \leq t \leq 2$ Notice that both C₁ and C₂ go from (0, 0)to (2, 2), but is $I _ { 1 } = I _ { 2 } ?$ Explain.