Evaluate the Surface Integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 155

Multiple Choice

Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = x \mathbf { i } + y \mathbf { j } + x \mathbf { k }$ and S is the part of the plane $z = 1 - x - y$ in the first octant with downward orientation.

• A) \(\frac { 1 } { 3 }\)
• B) \(\frac { 1 } { 2 }\)
• C) \(\frac { 1 } { 4 }\)
• D)\(1\)
• E) \(- \frac { 1 } { 3 }\)
• F)\(- \frac { 1 } { 2 }\)
• G)\(- \frac { 1 } { 4 }\)
• H)\(- 1\)

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