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

Essay

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ where $\mathbf { F } ( x , y ) = \left( y e ^ { x y } + \sin y \right) \mathbf { i } + \left( x e ^ { x y } + x \cos y \right) \mathbf { j }$ and C is the curve $x = \sqrt { 3 \cos t + 1 }$ , $y = 2 \sin ^ { 3 } t$ , $0 \leq t \leq \frac { \pi } { 2 }$ .