Evaluate the Integral in Terms of an Inverse Hyperbolic Function $$\int _ { 1 / 7 } ^ { 2 / 11 } \frac { d x } { x \sqrt { 25 - 64 x ^ { 2 } } }$$

question 145

Multiple Choice

Evaluate the integral in terms of an inverse hyperbolic function.
- $$\int _ { 1 / 7 } ^ { 2 / 11 } \frac { d x } { x \sqrt { 25 - 64 x ^ { 2 } } }$$

• A) \(- \frac { 1 } { 5 } \operatorname { sech } ^ { - 1 } \left( \frac { 16 } { 55 } \right) + \frac { 1 } { 5 } \operatorname { sech } ^ { - 1 } \left( \frac { 8 } { 35 } \right)\)
• B) \(\frac { 1 } { 5 } \tanh ^ { - 1 } \left( \frac { 20 } { 11 } \right) - \frac { 1 } { 5 } \tanh ^ { - 1 } \left( \frac { 5 } { 56 } \right)\)
• C) \(\frac { 1 } { 5 } \tanh ^ { - 1 } \left( \frac { 16 } { 55 } \right) - \frac { 1 } { 5 } \tanh ^ { - 1 } \left( \frac { 8 } { 35 } \right)\)
• D) \(- \frac { 1 } { 5 } \operatorname { sech } ^ { - 1 } \left( \frac { 5 } { 11 } \right) + \frac { 1 } { 5 } \operatorname { sech } ^ { - 1 } \left( \frac { 5 } { 56 } \right)\)

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Confidence Interval

A span of numbers obtained from sample observations, expected to encompass the value of an unseen population characteristic.

Null Hypothesis

A statement or hypothesis that indicates no statistical significance or effect, essentially asserting that any observed differences are due to chance.

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Alpha level, often denoted as α, is a threshold value used in statistics to determine the significance of a result, especially in hypothesis testing; it represents the probability of erroneously rejecting the null hypothesis.