Let And Let S Be the Surface with Equation $x ^ { 4 } + y ^ { 4 } + z ^ { 4 } = 1$

Short Answer

Let $\mathbf { F } ( x , y , z ) = \left( x + e ^ { y \tan z } \right) \mathrm { i } + 3 \mathrm { xe } ^ { x z } \mathbf { j } + ( \cos y - z ) \mathbf { k }$ and let S be the surface with equation $x ^ { 4 } + y ^ { 4 } + z ^ { 4 } = 1$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .