Evaluate the Line Integral Along the Curve C $\int _ { C } \frac { x + y + z } { 5 } d s , C$

question 273

Multiple Choice

Evaluate the line integral along the curve C.
- $\int _ { C } \frac { x + y + z } { 5 } d s , C$ is the curve $r ( t ) = 4 t i + \left( 6 \cos \frac { 1 } { 2 } t \right) j + \left( 6 \sin \frac { 1 } { 2 } t \right) k , 0 \leq t \leq 2 \pi$

• A) \(8 \pi ^ { 2 } + 48\)
• B) \(8 \pi\)
• C) \(8 \pi ^ { 2 } + 24\)
• D) \(8 + 24\)

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Definitions:

Protein Capsid

The protein shell of a virus, which encloses its genetic material and is critical for its ability to infect host cells.

Genome

Sum of all the genetic information in a cell or organism.

Host Specificity

The degree to which a parasite or pathogen can infect only a limited range of host species.

Intracellular Parasites

Intracellular parasites are organisms that live within the cells of their host, relying on their host's resources for survival, often causing disease.