Question Number 55702 by ajfour last updated on 02/Mar/19
$${s}=\int_{\mathrm{0}} ^{\:{x}} \sqrt{\mathrm{1}+\left(\mathrm{3}{t}^{\mathrm{2}} +{p}\right)^{\mathrm{2}} }{dt}\:\:=\:? \\ $$$$\:\:\:\:{take}\:{p}=\mathrm{1}\:\:{for}\:{a}\:{special}\:{case}. \\ $$
Commented by rahul 19 last updated on 03/Mar/19
$${I}\:{think}\:{for}\:{p}=\mathrm{1}\:{you}\:{can}\:{solve}\:{by}\:{using} \\ $$$${Newton}−{Leibneitz}\:{and}\:{then}\:{integrate}. \\ $$$$\left({Although}\:{little}\:{lengthy}\right)! \\ $$
Commented by mr W last updated on 03/Mar/19
$${is}\:{this}\:{not}\:{an}\:{ellipic}\:{integral}\:{which}\:{can} \\ $$$${not}\:{be}\:{solved}\:{in}\:{elementary}\:{functions}? \\ $$
Commented by mr W last updated on 03/Mar/19
$${no}!\:{we}\:{can}'{t}!\:{it}\:{is}\:{not}\:{to}\:{find}\:{a}\:{value}, \\ $$$${but}\:{to}\:{find}\:{a}\:{function}\:{s}\left({x}\right). \\ $$
Commented by maxmathsup by imad last updated on 03/Mar/19
$${the}\:{rmark}\:{of}\:{sir}\:{mrw}\:{is}\:{true}\:{because}\:{s}\:{is}\:{a}\:{function}\:{of}\:{x}\:{not}\:{a}\:{constant}\:{value}… \\ $$
Commented by ajfour last updated on 03/Mar/19
$${thanks}\:{everyone}\:{for}\:{checking} \\ $$$${such}\:{is}\:{the}\:{case}. \\ $$