Use Stokes's Theorem to Evaluate $\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49$

question 64

Multiple Choice

Use Stokes's Theorem to evaluate $\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49$ and $S$ is the first-octant portion of $z = x ^ { 2 }$ over $x ^ { 2 } + y ^ { 2 } = 49$
Use a computer algebra system to verify your result.

• A) \(\frac { 16,807 } { 15 }\)
• B) \(- \frac { 16,807 } { 15 }\)
• C) \(- \frac { 33,614 } { 15 }\)
• D) 0
• E) \(\frac { 33,614 } { 15 }\)

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