Category: Integration

Question Number 208805 by Mastermind last updated on 23/Jun/24 $$\mathrm{Integrate}:$$$$(\mathrm{xdz}-\mathrm{zdx})-{\mathrm{a}}^2(2\mathrm{xzdz}-{\mathrm{z}}^2\mathrm{dx})+{2\mathrm{x}}^3=0$$ Commented by mr W last updated on 23/Jun/24…

Question Number 208693 by Frix last updated on 21/Jun/24 $$\mathrm{Calculate}\mathrm{the}\mathrm{area}\mathrm{enclosed}\mathrm{by}\mathrm{the}\mathrm{curve}$$$${(\frac{1}{x}-2)}^2+{(\frac{1}{y}-2)}^2=1$$ Answered by mr W last updated on 21/Jun/24 $$\frac{\mathrm{1}}{{x}}−\mathrm{2}={u}\:\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{2}+{u}}…

Question Number 208661 by efronzo1 last updated on 20/Jun/24 $$\downharpoonleft \underset{―}{}$$ Answered by Berbere last updated on 20/Jun/24 $$3x+4=u\Rightarrow dx=\frac{du}{3}$$$$\int_{\mathrm{10}} ^{\mathrm{25}} {f}\left({u}\right).\frac{{du}}{\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}\left\{.\int_{\mathrm{10}} ^{\mathrm{15}}…

Question Number 208632 by necx122 last updated on 19/Jun/24 $$\int e^{-x^2}dx$$$$couldthisbeintegratedbypart?What$$$$approachwouldmostlikelybesuitable$$$$forthisintegral?$$$$$$ Commented by Tinku…

Question Number 208423 by lepuissantcedricjunior last updated on 15/Jun/24 $$\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{u}\mathit{l}\mathit{o}\mathit{n}\mathit{s}$$$$\mathit{i}=\int \int {\int }_{[0;1]}\frac{\mathit{d}\mathit{x}\mathit{d}\mathit{y}\mathit{d}\mathit{z}}{1-\mathit{x}\mathit{y}\mathit{z}}$$ Answered by Berbere last updated on 15/Jun/24 $$=\int \int [-\frac{1}{xy}ln(1-xy)]dydx$$$${xy}={u}\Rightarrow{dy}=\frac{{du}}{{x}}…