Use Long Division to Evaluate the Integral $$\int _ { 0 } ^ { 1 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 36 x + 1 } { x ^ { 2 } + 4 x - 12 } d x$$

question 59

Multiple Choice

Use long division to evaluate the integral. $$\int _ { 0 } ^ { 1 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 36 x + 1 } { x ^ { 2 } + 4 x - 12 } d x$$ The choices are rounded to 3 decimal places.

• A) \(- 3.544\)
• B) \(6.456\)
• C) \(1.456\)
• D) \(- 8.544\)
• E) \(11.456\)

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Definitions:

Tiny Bones

The three smallest bones in the human body, located in the middle ear, known as the malleus, incus, and stapes; vital for transmitting sound vibrations.

Middle Ear

The section of the ear between the eardrum and the oval window that amplifies sound waves and transmits them to the inner ear.

Conduction Deafness

A type of hearing loss caused by a problem in the transmission of sound waves through the outer ear or middle ear.

Sensory-Neural Deafness

A type of hearing loss that occurs due to damage to the inner ear or the nerve pathways from the inner ear to the brain.