Use Stoke's Theorem to Calculate the Surface Integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S } ,$

Use Stoke's theorem to calculate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S } ,$ where $\mathbf { F } ( x , y , z ) = \left( e ^ { x } \sin y \right) \mathbf { i } + \left( e ^ { x } \cos y - z \right) \mathbf { j } + y \mathbf { k }$ and S is the part of the cone $z ^ { 2 } = x ^ { 2 } + y ^ { 2 } + 3 \text { for which } 1 \leq z \leq 2$