Find the Centroid of the Region Bounded by the Graphs $$y = | x | \sqrt { 4 - x ^ { 2 } } , \quad y = 0 , \quad x = - 2 , \quad x = 2$$

question 109

Short Answer

Find the centroid of the region bounded by the graphs of the given equations.
$$y = | x | \sqrt { 4 - x ^ { 2 } } , \quad y = 0 , \quad x = - 2 , \quad x = 2$$

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Definitions:

Hemispheric Lateralization

The distinction between the functional specializations of the human brain's left and right hemispheres, such as language in the left and spatial abilities in the right.

Left-Brain

The left hemisphere of the brain, often associated with analytical thought, logic, language, and mathematical processes.

Right-Brain

The hemisphere of the brain that is often associated with creative and intuitive processes, spatial abilities, and the appreciation of music and art.

Empirical

Established through what is observed or encountered rather than through theoretical understanding or logical analysis.