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) \(\frac { 3 } { 8 } ( 2 \pi - 3 \sqrt { 3 } )\)

---

Definitions:

Negative Emotions

Negative emotions are feelings that are typically considered to be unpleasant or adverse, such as sadness, anger, or fear.

Diagnosis

The identification of the nature of an illness or other problem through examination of the symptoms.

Poverty and Race

The term "Poverty and Race" explores the intersectionality between socioeconomic status and racial or ethnic identity, often examining how they contribute to disparities in health, education, and opportunity.

Complete Remission

A state in which all signs and symptoms of a disease are absent, often used in the context of cancer to describe periods where the disease is undetectable.