Find the Length of the Curve $\mathbf { r } ( t ) = \left\langle \sin 2 t , \cos 2 t , 2 t ^ { \frac { 3 } { 2 } } \right\rangle 0 \leq t \leq 1$

question 34

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = \left\langle \sin 2 t , \cos 2 t , 2 t ^ { \frac { 3 } { 2 } } \right\rangle 0 \leq t \leq 1$

• A) \(\frac { 2 } { 27 } ( 13 \sqrt { 13 } - 8 )\)
• B) \(\frac { 13 } { 9 }\)
• C) \(\frac { 13 \sqrt { 13 } - 6 } { 27 }\)
• D) \(\frac { 16 } { 9 }\)
• E) \(\frac { 10 } { 27 } ( \sqrt { 13 } - 2 )\)
• F) \(\frac { 19 } { 9 }\)
• G) \(\frac { 4 } { 9 } ( 7 \sqrt { 7 } - 2 )\)
• H) \(\frac { 22 } { 9 }\)

---

Definitions:

Glutamic Acid

An amino acid used by the body to build proteins, also functioning as a neurotransmitter in the brain.

Aspartic Acid

Aspartic acid is a nonessential amino acid used in the biosynthesis of proteins, playing roles in the body's metabolic processes and neurotransmission.

MSG

Monosodium glutamate, a flavor enhancer commonly used in food preparation and processed foods.

Microvilli

Tiny, hair-like projections on the surface of some cells that increase surface area for absorption or secretion.