Question Number 25307 by NECx last updated on 08/Dec/17
$${An}\:{object}\:{constrained}\:{to}\:{move} \\ $$$${along}\:{the}\:{x}-{axis}\:{is}\:{acted}\:{upon}\:{by} \\ $$$${a}\:{force}\:{F}\left({x}\right)\:{where}\:{a}=\mathrm{5}{N}/{m}, \\ $$$${b}=−\mathrm{2}{N}/{m}.\:{F}\left({x}\right)={ax}+{bx}^{\mathrm{2}} \\ $$$${The}\:{object}\:{is}\:{observed}\:{to}\:{proceed} \\ $$$${directly}\:{from}\:{x}=\mathrm{1}{m}\:{to}\:{x}=\mathrm{3}{m}. \\ $$$${How}\:{much}\:{work}\:{was}\:{done}\:{by}\:{the} \\ $$$${object}\:{by}\:{the}\:{force}?{Does}\:{the} \\ $$$${process}\:{of}\:{integration}\:{take}\:{into} \\ $$$${account}\:{the}\:{fact}\:{that}\:{the}\:{force} \\ $$$${F}\left({x}\right)\:{changes}\:{sign}\:{in}\:{interval}. \\ $$