Use Reduction Formulas to Evaluate the Integral $\int \sin ^ { 2 } 3 x \cos ^ { 2 } 3 x d x$

question 452

Multiple Choice

Use reduction formulas to evaluate the integral.
- $\int \sin ^ { 2 } 3 x \cos ^ { 2 } 3 x d x$

• A) \(- \frac { 1 } { 3 } \sin 3 x \cos ^ { 3 } 3 x + \frac { x } { 8 } + \frac { 1 } { 3 } \sin 6 x + C\)
• B) \(- \frac { 1 } { 12 } \sin 3 x \cos ^ { 2 } 3 x + \frac { x } { 8 } + \frac { 1 } { 48 } \sin 6 x + C\)
• C) \(- \frac { 1 } { 12 } \sin 3 x \cos ^ { 3 } 3 x + \frac { x } { 8 } + \frac { 1 } { 48 } \sin 6 x + C\)
• D) \(- \frac { 1 } { 12 } \sin 3 x \cos ^ { 3 } 3 x + \frac { x } { 8 } + \frac { 1 } { 48 } \cos 6 x + C\)

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Definitions:

Predetermined Overhead Rate

An estimated rate used to allocate manufacturing overhead to individual products or job orders based on a certain activity base, such as machine hours or labor hours.

Machine-Hours

A unit of measure that represents the operational time of a machine, used in allocating manufacturing overhead based on the time machines are run.

Plantwide Predetermined

A rate, often related to overhead costs, that is set before the accounting period begins and applied uniformly throughout an entire plant or organization.

Machine-Hours

A measure of production output or activity level using the total hours machines are operated.