Find the Exact Value Of $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

Short Answer

Find the exact value of $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ where $\mathbf { F } ( x , y ) = e ^ { x - 1 } \mathbf { i } + x y \mathbf { j }$ and C is given by $\mathbf { r } ( t ) = 2 t ^ { 2 } \mathbf { i } + 7 t ^ { 3 } \mathbf { j } , 0 \leq t \leq 1$