Use Stokes' Theorem to Calculate the Circulation of the Field $\mathbf { F } = - 9 \mathrm { y } ^ { 3 } \mathbf { i } + 9 \mathrm { x } ^ { 3 } \mathbf { j } + 8 \mathrm { z } ^ { 3 } \mathbf { k }$

question 275

Multiple Choice

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
- $\mathbf { F } = - 9 \mathrm { y } ^ { 3 } \mathbf { i } + 9 \mathrm { x } ^ { 3 } \mathbf { j } + 8 \mathrm { z } ^ { 3 } \mathbf { k }$ ; C: the portion of the paraboloid $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = \mathrm { z }$ cut by the cylinder $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 4$

• A) \(- 432 \pi\)
• B) \(- 216 \pi\)
• C) \(432 \pi\)
• D) \(216 \pi\)

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