Evaluate the Integral by Using Multiple Substitutions $\int \frac { 3 \sin ^ { 2 } \sqrt { 3 y + 9 } \cos \sqrt { 3 y + 9 } } { 2 \sqrt { 3 y + 9 } } d y$

question 175

Multiple Choice

Evaluate the integral by using multiple substitutions.
- $\int \frac { 3 \sin ^ { 2 } \sqrt { 3 y + 9 } \cos \sqrt { 3 y + 9 } } { 2 \sqrt { 3 y + 9 } } d y$

• A) \(2 \sin \sqrt { 3 y + 9 } + C\)
• B) \(\frac { \sin ^ { 3 } \sqrt { 3 y + 9 } } { 18 } + C\)
• C) \(\frac { \sin ^ { 3 } \sqrt { 3 y + 9 } } { 3 } + C\)
• D) \(\frac { \sqrt { 3 y + 9 ^ { 3 } } } { 3 } + C\)

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Definitions:

Withdrawal Reflex

A spinal reflex that causes immediate withdrawal from a painful or harmful stimulus.

Interneurons

Neurons that transmit impulses between other neurons, especially as part of reflex arcs in the nervous system.

Endorphins

Natural pain-relieving peptides produced by the brain that also enhance feelings of pleasure.

Parasympathetic Nervous System

Part of the autonomic nervous system responsible for conserving energy and slowing the heart rate, facilitating a state of calm and relaxation.