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Find the Length of the Curve r(t)=2ti+t2j+lntk,1te3\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 3 }

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Find the length of the curve r(t) =2ti+t2j+lntk,1te3\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 3 }
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Definitions:

Hemoglobin

A protein found in red blood cells responsible for transporting oxygen from the lungs to the rest of the body and returning carbon dioxide from the tissues back to the lungs.

Oxygenated

Refers to compounds or blood enriched with oxygen.

Common Poison

Substances that can cause harm or death when introduced to a living organism's body in sufficient quantities.

Hemoglobin

A protein in red blood cells that carries oxygen from the lungs to the body's tissues and returns carbon dioxide from the tissues back to the lungs.

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