Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

Short Answer

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $\mathbf { F } ( x , y ) = e ^ { x } \mathbf { i } + x y \mathbf { j }$ and the curve $C$ is given by the vector function $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 0 \leq t \leq 1$ .