Category: Integration

Question Number 142475 by cherokeesay last updated on 01/Jun/21 Answered by qaz last updated on 01/Jun/21 $$\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+{\mathrm{x}}^2\mathrm{f}\left(\mathrm{x}\right)=0$$$$\Rightarrow \mathrm{f}\left(\mathrm{x}\right)+\frac{1}{{\mathrm{x}}^2}\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=0$$$$\mathrm{I}=\int_{\frac{\mathrm{1}}{\mathrm{x}}} ^{\mathrm{x}} \mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}=\int_{\mathrm{x}}…

Question Number 142457 by ajfour last updated on 01/Jun/21 $$I=\int \frac{dx}{\sqrt{a^2-(x+\frac{1}{x})}}$$ Answered by MJS_new last updated on 01/Jun/21 $${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{afraid}{\mathrm{you}}^{\prime }\mathrm{re}\mathrm{ending}\mathrm{on}\mathrm{elliptic}\mathrm{functions}$$$$\mathrm{again}.$$$$\mathrm{my}\:\mathrm{try}:…

Question Number 76913 by Ajao yinka last updated on 31/Dec/19 Answered by ~blr237~ last updated on 01/Jan/20 $$\mathrm{let}\mathrm{it}\mathrm{be}\mathrm{A}$$$$1+\mathrm{x}+\dots .+{\mathrm{x}}^{100}=\frac{1-{\mathrm{x}}^{101}}{1-\mathrm{x}}$$$$\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 142438 by rs4089 last updated on 31/May/21 $${\int }_0^1\frac{1-x}{lnx}dx$$$$howmanytrickssolvethis$$ Answered by Dwaipayan Shikari last updated on 31/May/21 $${log}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)…

Question Number 11352 by tawa last updated on 21/Mar/17 $$\mathrm{if},\mathrm{A}={\mathrm{x}}^2\sin \mathrm{yi}+{\mathrm{z}}^2\cos \mathrm{yj}-{\mathrm{xy}}^2\mathrm{k},\mathrm{find},\mathrm{dA}$$ Answered by sm3l2996 last updated on 22/Mar/17 $$\mathrm{dA}=\left(\mathrm{2xsin}\left(\mathrm{y}\right)\mathrm{i}−\mathrm{y}^{\mathrm{2}} \mathrm{k}\right)\mathrm{dx}+\left(\mathrm{x}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{y}\right)\mathrm{i}−\mathrm{z}^{\mathrm{2}}…