Use Reduction Formulas to Evaluate the Integral $$\int \csc ^ { 4 } \frac { t } { 5 } d t$$

question 204

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int \csc ^ { 4 } \frac { t } { 5 } d t$$

• A) \(- \frac { 5 } { 3 } \csc ^ { 3 } \frac { t } { 5 } \cot \frac { t } { 5 } + \frac { 10 } { 3 } \cot \frac { t } { 5 } + C\)
• B) \(- \frac { 1 } { 15 } \csc ^ { 2 } \frac { \mathrm { t } } { 5 } \cot \frac { \mathrm { t } } { 5 } - \frac { 2 } { 15 } \cot \frac { \mathrm { t } } { 5 } + \mathrm { C }\)
• C) \(- \frac { 5 } { 3 } \csc ^ { 2 } \frac { \mathrm { t } } { 5 } \cot \frac { \mathrm { t } } { 5 } - \frac { 10 } { 3 } \csc \frac { \mathrm { t } } { 5 } + \mathrm { C }\)
• D) \(- \frac { 5 } { 3 } \csc ^ { 2 } \frac { \mathrm { t } } { 5 } \cot \frac { \mathrm { t } } { 5 } - \frac { 10 } { 3 } \cot \frac { \mathrm { t } } { 5 } + \mathrm { C }\)

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Definitions:

Mean

The arithmetic average of a set of values, calculated by summing up all the values and then dividing by the number of values.

F Distribution

A probability distribution that arises in the analysis of variances for comparing sample variances or testing the hypothesis of equal variances, used primarily in ANOVA.

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution or equation, typically affecting the shape of the distribution.

Mean and Variance

Statistical measures where mean is the average of a set of numbers, and variance quantifies the spread of the numbers in the set.