Find the Length of the Curve $r = 3 \sin ^ { 3 } \left( \frac { \theta } { 3 } \right) , 0 \leq \theta \leq \frac { \pi } { 2 }$

question 363

Multiple Choice

Find the length of the curve.
-The curve $r = 3 \sin ^ { 3 } \left( \frac { \theta } { 3 } \right) , 0 \leq \theta \leq \frac { \pi } { 2 }$

• A) \(\frac { 9 } { 8 } ( 5 \pi - 8 )\)
• B) \(\frac { 9 } { 64 } ( 5 \pi - 9 \sqrt { 3 } )\)
• C) \(3 ( 3 \sqrt { 3 } - \pi )\)
• D) \(\frac { 3 } { 8 } ( 2 \pi - 3 \sqrt { 3 } )\)