Solve the Problem $$\int _ { 0 } ^ { \infty } \frac { \tan ^ { - 1 } \frac { x } { 3 } - \tan ^ { - 1 } \frac { x } { 5 } } { x } d x$$

question 328

Multiple Choice

Solve the problem.
-Evaluate
$$\int _ { 0 } ^ { \infty } \frac { \tan ^ { - 1 } \frac { x } { 3 } - \tan ^ { - 1 } \frac { x } { 5 } } { x } d x$$
by writing the integrand as an integral.

• A) \(\frac { \pi } { 4 } \ln \frac { 5 } { 6 }\)
• B) \(\ln \frac { 3 } { 5 }\)
• C) \(\frac { \pi } { 4 } \ln \frac { 5 } { 3 }\)
• D) \(\frac { \pi } { 2 } \ln \frac { 5 } { 3 }\)

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Definitions:

Sample Sizes

The count of data points or items chosen from a larger group for the purpose of statistical examination.

Pooled-variances T-test

A statistical method for comparing the means of two populations when it is assumed that both populations have equal variances.

Population Variances

A measure of the spread of a population's values, indicating how much the members of the population differ from the population mean.

Population Means

The average value of a set of characteristics within a total population.