Find $\int _ { C } \vec { F } \cdot d \vec { r }$

Essay

Find $\int _ { C } \vec { F } \cdot d \vec { r }$ of the function over the given curve: $\vec { F } ( x , y ) = \langle y , y \rangle$ and the curve C is given by $y = x ^ { 3 } , 0 \leq x \leq 2$