Evaluate the Line Integral Along the Curve C $\int _ { C } \left( \frac { 4 } { z } \right) ^ { 1 / 3 } \mathrm { ds } , \mathrm { C }$

question 264

Multiple Choice

Evaluate the line integral along the curve C.
- $\int _ { C } \left( \frac { 4 } { z } \right) ^ { 1 / 3 } \mathrm { ds } , \mathrm { C }$ is the curve $\mathbf { r } ( \mathrm { t } ) = \left( 4 \mathrm { t } ^ { 3 } \cos \mathrm { t } \right) \mathbf { i } + \left( 4 \mathrm { t } ^ { 3 } \sin \mathrm { t } \right) \mathbf { j } + 4 \mathrm { t } ^ { 3 } \mathbf { k } , 0 \leq \mathrm { t } \leq 3 \sqrt { 2 }$

• A) \(36 ( 4 - \sqrt { 2 } )\)
• B) \(72 ( 4 + \sqrt { 2 } )\)
• C) 0
• D) \(72 ( 4 - \sqrt { 2 } )\)

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