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Question Number 57491 by Joel578 last updated on 05/Apr/19

If R is a region enclosed by y = f(x), y = g(x), x = a, x = b,  is it possible to have f(x) and g(x) such that  the center of gravity (x^� , y^� ) is not inside R ?

$$\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{by}\:{y}\:=\:{f}\left({x}\right),\:{y}\:=\:{g}\left({x}\right),\:{x}\:=\:{a},\:{x}\:=\:{b}, \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{have}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{gravity}\:\left(\bar {{x}},\:\bar {{y}}\right)\:\mathrm{is}\:\mathrm{not}\:\mathrm{inside}\:{R}\:? \\ $$

Answered by ajfour last updated on 05/Apr/19

yes, say in boomerang shape.

$$\mathrm{yes},\:\mathrm{say}\:\mathrm{in}\:\mathrm{boomerang}\:\mathrm{shape}. \\ $$

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