Use Stokes' Theorem to Calculate the Circulation of the Field $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$

question 109

Multiple Choice

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
- $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$ the counterclockwise path around the perimeter of the triangle in the $x - y$ plane formed from the $x$ -axis, $y$ -axis, and the line $y = 5 - 4 x$

• A) \(\frac { 75 } { 2 }\)
• B) \(\frac { 15 } { 4 }\)
• C) \(- \frac { 75 } { 2 }\)
• D) \(\frac { 75 } { 4 }\)

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