Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k }$

question 22

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k }$ $1 \leq t \leq e ^ { 3 }$

• A) \(e ^ { 6 }\)
• B) \(e ^ { 3 }\)
• C) \(e ^ { 6 } + 2\)
• D) \(e ^ { 3 } + 2\)

---

Definitions:

Phage Release

The process by which bacteriophages (viruses that infect bacteria) exit the host cell after replicating, often resulting in the cell's lysis.

Penetration

The action or process of making a way through or into something.

Phage Therapy

The therapeutic use of bacteriophages to treat pathogenic bacterial infections.

Antibiotic Resistance

The ability of microorganisms to withstand the effects of antibiotics, making standard treatments ineffective.