Solve the Problem $$\int _ { 0 } ^ { \infty } \frac { \sin a x } { x } d x , a > 0$$

question 383

Multiple Choice

Solve the problem.
-Evaluate
$$\int _ { 0 } ^ { \infty } \frac { \sin a x } { x } d x , a > 0$$
by integrating
$$\int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } e ^ { - x y } \sin a x d A$$

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

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Definitions:

Phobic Disorder

An anxiety disorder characterized by excessive and persistent fear of a specific object, situation, or activity, leading to avoidance behavior.

Generalised Anxiety Disorder

A chronic disorder characterized by excessive, long-lasting anxiety and worry about nonspecific life events, objects, and situations.

Obsessive-Compulsive Disorder

A mental disorder characterized by repetitive, unwanted thoughts (obsessions) and irrational, excessive urges to do certain actions (compulsions).

Conversion Disorder

A mental health condition where a person has blindness, paralysis, or other nervous system symptoms that cannot be explained by medical evaluation.