Use Reduction Formulas to Evaluate the Integral $$\int \cot ^ { 4 } 3 x d x$$

question 5

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int \cot ^ { 4 } 3 x d x$$

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

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Definitions:

Sensorimotor

A stage in Jean Piaget's theory of cognitive development where infants from birth to about 2 years old understand the world through sensory experiences and their motor actions.

Concrete Operational

A stage in Piaget's theory of cognitive development, where children aged 7-12 start to think logically about concrete events and understand the concept of conservation.

Sensorimotor

Pertaining to the developmental stage in infants where they learn to perceive and interact with the world through their senses and motor actions.

Acute Medical Condition

A sudden onset of a disease or disorder that requires immediate care, typically characterized by severe and abrupt symptoms.