Category: Integration

Question Number 136841 by physicstutes last updated on 26/Mar/21 $$\int \sqrt{x^2+1}dx=?$$ Answered by Olaf last updated on 26/Mar/21 $$\mathrm{F}\left(x\right)=\int \sqrt{x^2+1}dx$$$$\mathrm{F}\left({u}\right)\:\:\overset{{x}=\mathrm{sh}{u}} {=}\:\:\int\sqrt{\mathrm{sh}^{\mathrm{2}}…

Question Number 136813 by mnjuly1970 last updated on 26/Mar/21 $$$$$$\dots \dots advancedcalculus\left(I\right)\dots .$$$$if:$$$$\mathrm{\Omega }={\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}\frac{x.cos\left(2x\right).cos\left(x\right)}{{sin}^7\left(x\right)}dx=\frac{a\pi }{90}$$$$then::a=???$$$$$$$$\:\:\:\:…

Question Number 136803 by mnjuly1970 last updated on 26/Mar/21 $$$$$$\dots ..\mathcal{A}dvanced◂\dots \dots \dots \dots .▸\mathcal{C}alculus\dots ..$$$$\mathit{\varphi }={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{sin\left(\frac{1}{x^3}\right)}{x}dx=\dots \dots ???$$$$solution::$$$$\:\:\:\:\:\:\boldsymbol{\phi}\overset{\frac{\mathrm{1}}{{x}}\:={t}} {=}\:\mathrm{2}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}^{\mathrm{3}} \right)}{\frac{\mathrm{1}}{{t}}}.\frac{{dt}}{{t}^{\mathrm{2}}…

Question Number 136762 by snipers237 last updated on 25/Mar/21 $$letC(a,r)=\{z\in \mathbb{C},\mid z-a\mid =r\}$$$$Letu,v,w\in C(a,r)suchasu+v=2w$$$$Provethat\frac{u-a}{v-a}=1,u=v=w$$$$$$$$Itshowsthatthemiddleofasegment$$$$joiningtwopointsinacircleisnotinthatcircle$$ Terms of Service…

Question Number 136750 by mnjuly1970 last updated on 25/Mar/21 $$\dots ..advancedcalculus\dots ..$$$$provethat::$$$$\dots \mathit{\varphi }={\int }_0^{\mathrm{\infty }}\frac{1-e^{-x^2}}{x^2}dx=\sqrt{\pi }$$ Answered by Ñï= last…