$\text { Determine whether the improper integral } \int _ { 7 } ^ { 8 } \frac { 1 } { \sqrt { 64 - x ^ { 2 } } } d x \text { diverges or converges. }$

question 18

Multiple Choice

$\text { Determine whether the improper integral } \int _ { 7 } ^ { 8 } \frac { 1 } { \sqrt { 64 - x ^ { 2 } } } d x \text { diverges or converges. }$ Evaluate the integral if it converges.

• A) \(\frac { \pi } { 2 } - \arcsin \left( \frac { 7 } { 8 } \right)\)
• B) \(\frac { \pi } { 16 } - \arcsin \left( \frac { 7 } { 8 } \right)\)
• C) \(\frac { \pi } { 2 } - \arcsin \left( \frac { 7 } { 64 } \right)\)
• D) \(\frac { \pi } { 16 } - \arcsin \left( \frac { 7 } { 64 } \right)\)
• E) diverges

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Definitions:

Statistical Technique

A method or procedure applied to data collection, analysis, interpretation, and presentation in statistical studies.

Molecular Genetic Studies

Studies of the structure and function of genes that help in understanding how genetic mutations can lead to disease.

Genetic Abnormalities

Variations from the normal sequence in the genetic material of an organism, which may or may not lead to disease or conditions.

Psychopathology

Investigating mental illnesses, covering their manifestations, reasons, and healing approaches.