The Base of a Certain Solid Is a Plane Region $y = 1 - x ^ { 2 }$

question 141

Short Answer

The base of a certain solid is a plane region R enclosed by the x-axis and the curve $y = 1 - x ^ { 2 }$ . Each cross-section of the solid perpendicular to the y-axis is an isosceles right triangle with hypotenuse lying in R. Find the volume of the solid.

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Definitions:

Proteins

Large, complex molecules made up of amino acids, essential to the structure, function, and regulation of the body's tissues and organs.

Glucostatic Theory

A theory suggesting that blood glucose levels regulate feelings of hunger and satiety.

Blood Glucose

The sugar that is transported through the bloodstream to supply energy to cells throughout the body; it is critical for metabolic processes.

Hypothalamus

A region of the brain responsible for producing hormones that control body temperature, hunger, moods, release of hormones from many glands, especially the pituitary gland, and in regulating sleep cycles.