Question Number 170015 by Best1 last updated on 14/May/22
$${verify}\:{that}\:{the}\:{force}\: \\ $$$$\:{F}={xyi}+{xyj}+{yzk}\:{is} \\ $$$$\:{conservative} \\ $$
Answered by ajfour last updated on 14/May/22
$${dW}={xydx}+{xydy}+{yzdz} \\ $$$$\mathrm{2}{dW}={yd}\left({x}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right)+{yd}\left({z}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:={yd}\left({x}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:={yd}\left({s}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)+{xd}\left({y}^{\mathrm{2}} \right) \\ $$$$....!! \\ $$