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 $\mathbf { F } ( x , y , z ) = ( 2 x y + \ln z ) \mathbf { i } + \left( x ^ { 2 } + 1 + z \cos y z \right) \mathbf { j } + \left( \frac { x } { 2 } + y \cos y z \right) \mathbf { k }$ and C is the curve $x = \sqrt { 3 \cos t + 1 }$ , $y = 2 \sin ^ { 3 } t$ , $z = \sin t + \cos t$ , $0 \leq t \leq \frac { \pi } { 2 }$ .