Evaluate the Given Integral $$\int _ { 0 } ^ { 1 / 7 } \frac { 1 } { 1 + 49 x ^ { 2 } } d x$$

question 74

Multiple Choice

Evaluate the given integral. $$\int _ { 0 } ^ { 1 / 7 } \frac { 1 } { 1 + 49 x ^ { 2 } } d x$$

• A) \(\frac { \pi } { 35 }\)
• B) \(\frac { \pi } { 21 }\)
• C) \(\frac { \pi } { 14 }\)
• D) \(\frac { \pi } { 28 }\)

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Definitions:

Bottom-up Processing

A cognitive approach in which perception starts with stimuli input from the environment and works upwards to form a higher-level analysis.

Perceptual Constancy

The ability of the perceptual system to recognize objects as having constant properties (size, shape, color) even when sensory input varies.

Retinal Images

The projections of visual stimuli on the retina, the light-sensitive layer at the back of the eye, which are then processed by the brain to create visual perception.

Gestalt Principles

Theories in psychology that propose humans naturally perceive objects as organized patterns and wholes, rather than their separate components.