Evaluate the Integral Using the Given Substitution $$\int \left( 4 - \sin \frac { t } { 5 } \right) ^ { 2 } \cos \frac { t } { 5 } d t , \quad u = 4 - \sin \frac { t } { 5 }$$

question 192

Multiple Choice

Evaluate the integral using the given substitution.
- $$\int \left( 4 - \sin \frac { t } { 5 } \right) ^ { 2 } \cos \frac { t } { 5 } d t , \quad u = 4 - \sin \frac { t } { 5 }$$

• A) \(\frac { 1 } { 3 } \left( 4 - \sin \frac { t } { 5 } \right) ^ { 3 } \sin \frac { t } { 5 } + C\)
• B) \(5 \left( 4 - \sin \frac { t } { 5 } \right) ^ { 3 } + C\)
• C) \(\frac { 5 } { 3 } \left( 4 - \cos \frac { t } { 5 } \right) ^ { 3 } + C\)
• D) \(- \frac { 5 } { 3 } \left( 4 - \sin \frac { t } { 5 } \right) ^ { 3 } + C\)

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Definitions:

Objective Personality

Objective Personality refers to the assessment and analysis of personality based on measurable or observable traits, minimizing subjective interpretation.

NEO PI-3

A psychological personality inventory that measures five major domains of personality as well as six facets within each domain.

Projective Personality

This term refers to a type of personality test in which the test-taker is presented with a series of ambiguous stimuli or images and asked to interpret them, with the interpretation thought to reveal underlying aspects of the individual's personality.

Objective Personality

Personality assessments that measure traits using standardized methods, minimizing subjective interpretation by relying on direct, quantifiable measures.