Solve the Problem $$\int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } \frac { 1 } { \left( 4 + x ^ { 2 } + y ^ { 2 } \right) ^ { 5 } } d x d y$$

question 362

Multiple Choice

Solve the problem.
-Evaluate
$$\int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } \frac { 1 } { \left( 4 + x ^ { 2 } + y ^ { 2 } \right) ^ { 5 } } d x d y$$

• A) \(\frac { \pi } { 6144 }\)
• B) \(\frac { \pi } { 1536 }\)
• C) \(\frac { \pi } { 1024 }\)
• D) \(\frac { \pi } { 4096 }\)

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Definitions:

N1 Sleep

The first stage of the sleep cycle, characterized as the transition period from wakefulness to sleep, marked by light sleep and a reduction in muscle activity and awareness of the surroundings.

Circadian Rhythm

The internal biological clock that regulates the sleep-wake cycle and other physiological processes within approximately a 24-hour period.

Alpha Wave

A type of brain wave detected by electroencephalography (EEG) that indicates a state of physical and mental relaxation while being awake.

REM Rebound

The phenomenon where a person experiences increased amounts of REM sleep after being deprived of REM sleep in previous nights.