Evaluate the Integral $$\int x ^ { 5 } e ^ { - x ^ { 6 } } d x$$

question 59

Multiple Choice

Evaluate the integral.
- $$\int x ^ { 5 } e ^ { - x ^ { 6 } } d x$$

• A) \(- \frac { 1 } { 6 } e ^ { - x ^ { 7 } } + C\)
• B) \(- \frac { 1 } { 6 } e ^ { - x ^ { 6 } } + C\)
• C) \(- 6 e ^ { - x ^ { 7 } } + C\)
• D) \(\mathrm { e } ^ { - \mathrm { x } ^ { 6 } } + \mathrm { C }\)

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Definitions:

Equality Of Variances

The assumption that different groups or samples have similar variances, often a prerequisite for certain statistical tests.

Test Statistic

A numerical value calculated from a statistical test, used to determine whether to reject the null hypothesis.

Confidence Coefficient

The level of certainty, typically expressed as a percentage, associated with a confidence interval.

Null Hypothesis

A proposition in statistics that suggests no significant difference or effect exists between certain characteristics of a population.