Evaluate the Integral $\int _ { 0 } ^ { 2 } \frac { 12 x } { \left( 2 x ^ { 2 } + 1 \right) ^ { 2 } }$

question 175

Multiple Choice

Evaluate the integral.
- $\int _ { 0 } ^ { 2 } \frac { 12 x } { \left( 2 x ^ { 2 } + 1 \right) ^ { 2 } }$ dx

• A) \(\frac { 728 } { 19,683 }\)
• B) \(\frac { 8 } { 3 }\)
• C) \(\frac { 8 } { 27 }\)
• D) 2

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Definitions:

Temporal Lobes

The temporal lobes are regions of the brain that play key roles in processing auditory information and are involved in understanding language and storing memories.

Language Processing

The method by which the brain comprehends, interprets, and produces language, involving a complex interaction of cognitive processes.

Memory

The faculty by which the mind stores and remembers information, enabling learning and knowledge retention over time.

Hippocampus

A major component of the brain in humans and other animals, involved in the consolidation of information from short-term memory to long-term memory, and in spatial memory that enables navigation.