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-

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

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

Answered by ajfour last updated on 05/Apr/19

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

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