Category: Integration

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}}…

Question Number 208334 by Shrodinger last updated on 12/Jun/24 $${\int }_0^{\frac{4}{\pi }}ln\left(cosx\right)dx$$ Commented by Frix last updated on 12/Jun/24 $$\mathrm{This}\mathrm{question}\mathrm{has}\mathrm{been}\mathrm{answered}\left(208280\right)$$ Terms…

Question Number 208280 by Shrodinger last updated on 10/Jun/24 $$L={\int }_0^{\frac{4}{\pi }}ln\left(cosx\right)dx$$ Answered by Berbere last updated on 10/Jun/24 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{ln}\left(\frac{{cos}\left({x}\right)}{{sin}\left({x}\right)}.{sin}\left({x}\right){cos}\left({x}\right)\right){dx}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…