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Category: Integration

let-f-x-0-1-dt-1-xch-t-with-x-real-1-determine-a-explicit-form-of-f-x-2-find-also-g-x-0-1-dt-1-xch-t-2-3-calculate-0-1-dt-1-3ch-t-and-0-1-dt-1-3ch-t-

Question Number 59528 by Mr X pcx last updated on 11/May/19 letf(x)=01dt1+xch(t)withxreal1)determineaexplicitformoff(x)2)findalsog(x)=01dt(1+xch(t))2$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{ch}\left({t}\right)}\:{and}\:…

A-rescue-cable-attached-to-a-helicopter-s-weighs-2-lb-ft-A-man-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-th

Question Number 125052 by bramlexs22 last updated on 08/Dec/20 Arescuecableattachedtoahelicoptersweighs2lb/ft.Aman180lbgrabstheendoftheropeandhispulledfromtheoceanintothehelicopter.Howmuchworkisdoneinliftingthemanifthehelicopter$${is}\:\mathrm{40}\:{ft}\:{above}\:{the}\:{water}\:? \

dx-x-2-3x-4-

Question Number 125053 by bramlexs22 last updated on 08/Dec/20 dxx2+3x4=? 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}} \

It-takes-a-force-of-19-000-lb-to-compress-a-spring-from-its-free-height-of-15-in-to-its-fully-compressed-height-of-10-in-How-much-work-does-it-take-to-compress-the-spring-the-first-in-a-1900-in

Question Number 125048 by bemath last updated on 08/Dec/20 Ittakesaforceof19,000lbtocompressaspringfromitsfreeheightof15intoitsfullycompressedheightof10in.Howmuchworkdoesittaketocompressthespringthefirstin?(a)1900in.lb$$\left({b}\right)\:\mathrm{950}\:{in}.−{lb} \

Question-59509

Question Number 59509 by aliesam last updated on 11/May/19 Answered by MJS last updated on 11/May/19 cscπxdx=dxsinπx=[t=πxdx=dtπ]=1πdtsint=$$\:\:\:\:\:\left[{u}=\mathrm{tan}\:\frac{{t}}{\mathrm{2}}\:\rightarrow\:{dt}=\mathrm{2}\frac{{du}}{{u}^{\mathrm{2}} +\mathrm{1}}\right] \