Evaluate the Integral $$\int \frac { - \left( \cot ^ { - 1 } t \right) ^ { 7 } } { 1 + t ^ { 2 } } d t$$

question 119

Multiple Choice

Evaluate the integral.
- $$\int \frac { - \left( \cot ^ { - 1 } t \right) ^ { 7 } } { 1 + t ^ { 2 } } d t$$

• A) \(\sqrt { \cot ^ { - 1 } t } + C\)
• B) \(\frac { \left( \cot ^ { - 1 } t \right) ^ { 8 } } { 8 } + C\)
• C) \(7 \left( \cot ^ { - 1 } t \right) ^ { 6 } + C\)
• D) \(- 7 \left( \cot ^ { - 1 } t \right) ^ { 8 } + C\)

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Definitions:

Colored Part

The iris, the circular structure in the eye responsible for controlling the diameter and size of the pupils and thus the amount of light reaching the retina.

Pupil Size

The diameter of the circular opening in the center of the iris of the eye, which can vary in response to light exposure or emotional state.

Trichromatic Theory

Theory stating that color perception is produced by three types of cone receptors in the retina that are particularly sensitive to different, but overlapping, ranges of wavelengths.

Visual System

The part of the central nervous system that allows organisms to process visual detail, including the eye, optic nerve, and brain regions involved in vision.