Category: Integration

Question Number 187700 by cortano12 last updated on 20/Feb/23 $$Findminimumareaofthepart$$$$y=x^{2}andy=kx(x^2-k),k>0$$ Commented by cortano12 last updated on 21/Feb/23 Terms of…

Question Number 187703 by Tawa11 last updated on 20/Feb/23 $$\int \frac{1}{{5\mathrm{x}}^2-2\mathrm{x}-4}\mathrm{dx}$$ Answered by MikeH last updated on 20/Feb/23 $$=\frac{1}{5}\int \frac{1}{x^2-\frac{2}{5}x-\frac{4}{5}}dx$$$$=\:\frac{\mathrm{1}}{\mathrm{5}}\int\frac{\mathrm{1}}{\left({x}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{4}}{\mathrm{5}}}{dx}…

Question Number 122159 by mnjuly1970 last updated on 14/Nov/20 $$\dots nicecalculus\dots$$$$provethat::$$$$\mathrm{\Omega }={\int }_0^{\frac{\pi }{2}}\{{tan}^{-1}\left(ptan\left(x\right)\right)-{tan}^{-1}\left(qtan\left(x\right)\right)\}(tan\left(x\right)+cot\left(x\right))dx$$$$=\frac{\pi }{2}log\left(\frac{p}{q}\right)(p,q>0)$$$$m.n.$$ Answered…

Question Number 122137 by sdfg last updated on 14/Nov/20 Answered by Bird last updated on 14/Nov/20 $$\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dt$$$$\int_{−\infty} ^{+\infty} \:{e}^{{xt}−{e}^{{t}}…

Question Number 122108 by bemath last updated on 14/Nov/20 $$\underset{1}{\stackrel{2}{\int }}\frac{\ln \left(x\right)}{x^2}dx?$$ Answered by Dwaipayan Shikari last updated on 14/Nov/20 $$−\left[{log}\left({x}\right)\frac{\mathrm{1}}{{x}}\right]_{\mathrm{1}} ^{\mathrm{2}}…