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Trigonometry
Question

Archimedes' area formula for parabolic arches Arc...

Archimedes' area formula for parabolic arches Archimedes \(( 287 - 212\) B.c.), inventor, military engineer, physicist, and the greatest mathematician of classical times in the Western world, dis- covered that the area under a parabolic arch is two-thirds the base times the height. Sketch the parabolic arch \(y = h - ( 4 h / b ^ { 2 } ) x ^ { 2 }\) , \(- b / 2 \leq x \leq b / 2\) , assuming that \(h\) and \(b\) are positive. Then use calculus to find the area of the region enclosed between the arch and the \(x\) -axis.

Answer

\(\frac { 2 } { 3 } b h\)

Solution
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