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

question 327

Multiple Choice

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

• A) \(\frac { 3 a ^ { 2 } } { 16 }\)
• B) \(\frac { 3 \pi \mathrm { a } ^ { 2 } } { 16 }\)
• C) \(2 a\)
• D) \(2 \pi a\)

---

Definitions:

Initiate Movement

Initiate Movement pertains to the neurological process of starting any voluntary movement, involving the planning and execution phases in the brain.

Bodily Sensations

The feelings or perceptions that originate from the physical body, including touch, pain, temperature, or internal conditions.

Parietal Lobe

A region of the brain associated with processing sensory information concerning the body's position and navigation.

Frontal Lobe

The frontal lobe is a region in the brain involved in decision making, problem solving, control of purposeful behaviors, consciousness, and emotions.