Question Number 125052 by bramlexs22 last updated on 08/Dec/20 $$\:{A}\:{rescue}\:{cable}\:{attached}\:{to}\:{a}\: \\ $$$${helicopter}'{s}\:{weighs}\:\mathrm{2}\:{lb}/{ft}.\: \\ $$$${A}\:{man}\:\mathrm{180}−{lb}\:{grabs}\:{the}\:{end}\: \\ $$$${of}\:{the}\:{rope}\:{and}\:{his}\:{pulled}\: \\ $$$${from}\:{the}\:{ocean}\:{into}\:{the}\:{helicopter}. \\ $$$${How}\:{much}\:{work}\:{is}\:{done}\:{in}\: \\ $$$${lifting}\:{the}\:{man}\:{if}\:{the}\:{helicopter} \\ $$$${is}\:\mathrm{40}\:{ft}\:{above}\:{the}\:{water}\:? \\…
Question Number 125053 by bramlexs22 last updated on 08/Dec/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}}}\:=? \\ $$ Commented by Dwaipayan Shikari last updated on 08/Dec/20 $$\int\frac{{dx}}{\:\sqrt{\left({x}+\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} }}\:\:\:\:\:\:\:\:\:\:\:\:{x}+\frac{\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{5}}{\mathrm{2}}{sec}\theta\Rightarrow=\frac{\mathrm{5}}{\mathrm{2}}{sec}\theta{tan}\theta\frac{{d}\theta}{{dx}} \\…
Question Number 125050 by bramlexs22 last updated on 08/Dec/20 $$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{e}^{\mathrm{cos}\:{x}} }{{e}^{\mathrm{cos}\:{x}} +{e}^{−\mathrm{cos}\:{x}} }\:{dx}\:=?\: \\ $$ Answered by liberty last updated on 08/Dec/20 $${replace}\:{x}\:{by}\:\pi−{x}\:…
Question Number 125048 by bemath last updated on 08/Dec/20 $${It}\:{takes}\:{a}\:{force}\:{of}\:\mathrm{19},\mathrm{000}\:{lb}\:{to} \\ $$$${compress}\:{a}\:{spring}\:{from}\:{its}\:{free} \\ $$$${height}\:{of}\:\mathrm{15}\:{in}\:{to}\:{its}\:{fully}\: \\ $$$${compressed}\:{height}\:{of}\:\mathrm{10}\:{in}.\:{How} \\ $$$${much}\:\:{work}\:{does}\:{it}\:{take}\:{to}\: \\ $$$${compress}\:{the}\:{spring}\:{the}\:{first}\:{in}? \\ $$$$\left({a}\right)\:\mathrm{1900}\:{in}.−{lb} \\ $$$$\left({b}\right)\:\mathrm{950}\:{in}.−{lb} \\…
Question Number 59509 by aliesam last updated on 11/May/19 Answered by MJS last updated on 11/May/19 $$\int\mathrm{csc}\:\pi{x}\:{dx}=\int\frac{{dx}}{\mathrm{sin}\:\pi{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\pi{x}\:\rightarrow\:{dx}=\frac{{dt}}{\pi}\right] \\ $$$$=\frac{\mathrm{1}}{\pi}\int\frac{{dt}}{\mathrm{sin}\:{t}}= \\ $$$$\:\:\:\:\:\left[{u}=\mathrm{tan}\:\frac{{t}}{\mathrm{2}}\:\rightarrow\:{dt}=\mathrm{2}\frac{{du}}{{u}^{\mathrm{2}} +\mathrm{1}}\right] \\…
Question Number 59506 by tanmay last updated on 11/May/19 Commented by MJS last updated on 11/May/19 $${k}\:\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Commented by tanmay last updated on…
Question Number 59503 by ANTARES VY last updated on 11/May/19 $$\underset{\boldsymbol{{a}}} {\overset{\boldsymbol{{b}}} {\int}}\left(\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } \right)\boldsymbol{{dx}}=? \\ $$ Commented by Mr X pcx last updated on…
Question Number 125034 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{x}}{\mathrm{sinx}}\mathrm{dx} \\ $$ Commented by Olaf last updated on 07/Dec/20 $$\mathrm{The}\:\mathrm{Catalan}\:\mathrm{constant}\:\mathrm{K}\:\mathrm{has}\:\mathrm{many} \\…
Question Number 190552 by mathlove last updated on 05/Apr/23 $$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} {ln}\left(\frac{{ln}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{{ln}\left({x}^{\mathrm{2}} −{x}+\frac{\mathrm{17}}{\mathrm{6}}\right)}\right){dx}=? \\ $$ Commented by mathlove last updated on 06/Apr/23 $${any}\:{one}\:{solve}\:{this} \\ $$…
Question Number 59474 by rahul 19 last updated on 10/May/19 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\mathrm{10}\pi} \left(\left[\mathrm{sec}^{−\mathrm{1}} {x}\right]+\left[\mathrm{co}{t}^{−\mathrm{1}} {x}\right]\:\right)\:{dx}\:=\:? \\ $$$$\left.\mathrm{2}\right){area}\:{bounded}\:{by}\:{curve}\:{y}={ln}\left({x}\right)\:{and} \\ $$$${the}\:{lines}\:{y}=\mathrm{0},{y}={ln}\left(\mathrm{3}\right)\:{and}\:{x}=\mathrm{0}\:{is} \\ $$$${equal}\:{to}\:? \\ $$ Commented by…