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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Definitions:

Harry S. Truman

The 33rd President of the United States, serving from 1945 to 1953, known for implementing the Marshall Plan to rebuild the economy of Western Europe, and for leading the U.S. during the early Cold War.

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A prominent Soviet politician and diplomat known for his role in the Stalin administration, including as Foreign Minister.

Joseph Stalin

A Soviet political leader who served as general secretary of the Communist Party of the Soviet Union from 1922 until his death in 1953, known for his totalitarian rule and policies leading to massive industrialization and collectivization.

Truman's Revelation

Likely referring to significant policies or announcements made by Harry S. Truman, the 33rd President of the United States, but without more context, the specific revelation is unclear. NO.