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

question 276

Multiple Choice

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

• A) \(\frac { \pi } { 4 }\)
• B) \(\frac { \pi } { 3 }\)
• C) \(\frac { \pi } { 8 }\)
• D) \(\frac { \pi } { 5 }\)

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Definitions:

Vesicles

Small sacs within the synaptic knobs that contain chemicals called neurotransmitters.

Impulse Transmission

The process by which nerve cells communicate with each other or with muscles, involving the movement of electrical or chemical signals across synapses.

Diencephalon

A region of the brain located between the cerebrum and midbrain that includes the thalamus and hypothalamus, important for sensory and autonomic functions.

Cerebral Cortex

The cerebrum's external neural tissue layer, crucial for functions such as memory, attention, perception, thinking, awareness, thought, language, and consciousness.