Evaluate the Integral $$\int 2 \cos ^ { 3 } 3 x d x$$

question 13

Multiple Choice

Evaluate the integral.
- $$\int 2 \cos ^ { 3 } 3 x d x$$

• A) \(\frac { 2 } { 3 } \sin 3 x + \frac { 2 } { 9 } \sin ^ { 3 } 3 x + C\)
• B) \(\frac { 2 } { 3 } \sin 3 x - \frac { 2 } { 9 } \cos ^ { 3 } 3 x + C\)
• C) \(\frac { 2 } { 3 } \sin 3 x - \frac { 2 } { 9 } \sin ^ { 3 } 3 x + C\)
• D) \(2 \sin 3 x - \frac { 2 } { 3 } \sin ^ { 3 } 3 x + C\)

---

Definitions:

Carotenoids

A group of yellow to orange plant pigments synthesized from isoprene subunits; include carotenes and xanthophylls.

Vitamin A

An essential fat-soluble vitamin important for vision, growth, cell division, reproduction, and immunity.

Carotenoid

Pigments found in plants and some microorganisms, responsible for vibrant yellow, red, and orange colors and playing a role in photosynthesis.

Insoluble

A characteristic of substances that cannot dissolve in a specified solvent, such as water.