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

question 85

Multiple Choice

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

• A) \(\frac { 1 } { 3 } x ^ { 3 } \cos 3 x + \frac { 1 } { 3 } x ^ { 2 } \sin 3 x - \frac { 2 } { 9 } x \cos 3 x - \frac { 2 } { 27 } \sin 3 x + C\)
• B) \(\frac { 1 } { 3 } x ^ { 3 } \sin 3 x - \frac { 1 } { 3 } x ^ { 2 } \cos 3 x + \frac { 2 } { 9 } x \sin 3 x + \frac { 2 } { 27 } \cos 3 x + C\)
• C) \(\frac { 1 } { 3 } x ^ { 3 } \sin 3 x + 1 x ^ { 2 } \cos 3 x - 2 x \sin 3 x - 2 \cos 3 x + C\)
• D) \(\frac { 1 } { 3 } x ^ { 3 } \sin 3 x + \frac { 1 } { 3 } x ^ { 2 } \cos 3 x - \frac { 2 } { 9 } x \sin 3 x - \frac { 2 } { 27 } \cos 3 x + C\)

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Definitions:

Tension-Cohesion Model

A theory explaining the movement of water through plants, where water molecules stick together (cohesion) and are pulled up the plant through tension.

Gravity

The force that attracts a body toward the center of the earth, or any other physical body having mass.

Water Molecules

The smallest particle of water, made up of two hydrogen atoms bonded to one oxygen atom, essential for most forms of life.

Cohesive

The property of substances to stick together or the action of forming a united whole, often referring to the unity within a group or material.