Evaluate the Integral by Using Multiple Substitutions $$\int \frac { ( 2 r - 6 ) \cos \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } } { \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } } d r$$

question 292

Multiple Choice

Evaluate the integral by using multiple substitutions.
- $$\int \frac { ( 2 r - 6 ) \cos \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } } { \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } } d r$$

• A) \(\frac { 1 } { 12 } \sin \sqrt { 3 ( 2 r - 6 ) ^ { 2 } } + C\)
• B) \(\frac { \cos \sqrt { 3 r ^ { 2 } + 6 } } { 12 \sqrt { 3 r ^ { 2 } + 6 } } + C\)
• C) \(- \sin \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } + C\)
• D) \(\frac { 1 } { 6 } \sin \sqrt { 3 ( 2 r - 6 ) ^ { 2 } + 7 } + C\)

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Definitions:

Textiles

Materials that are woven or knitted, typically used for making clothes and other objects.

Ironworks

A place where iron is smelted, forged, or processed into finished products.

Cotton Gin

Invented by Eli Whitney in 1793, the machine that separated cotton seed from cotton fiber, speeding cotton processing and making profitable the cultivation of the more hardy, but difficult to clean, short-staple cotton; led directly to the dramatic nineteenth-century expansion of slavery in the South.

Eli Whitney

An American inventor best known for inventing the cotton gin, a device that revolutionized the cotton industry.