Category: Integration

Question Number 76143 by Master last updated on 24/Dec/19 Commented by mathmax by abdo last updated on 24/Dec/19 $$letI={\int }_0^1\sqrt{4+x^2}dxchangementx=2sh\left(t\right)give$$$${I}\:=\int_{\mathrm{0}} ^{{argsh}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}…

Question Number 10555 by paonky last updated on 17/Feb/17 $$\mathrm{why}\mathrm{\Gamma }\left(x\right)={\int }_0^1{[-\ln \left(\mathrm{u}\right)]}^{x-1}du?$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{how}\mathrm{to}\mathrm{prove}\mathrm{this}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 141623 by qaz last updated on 21/May/21 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}{\left({\int }_0^1\frac{x^n}{1+x}dx\right)}^2=ln2$$ Answered by mindispower last updated on 21/May/21…

Question Number 76052 by Ajao yinka last updated on 23/Dec/19 Commented by MJS last updated on 23/Dec/19 $$t={\mathrm{e}}^{-x}\to dx=-{\mathrm{e}}^{x}dt$$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{t}^{−{t}} {dt}\approx\mathrm{1}.\mathrm{291286}…

Question Number 141581 by qaz last updated on 20/May/21 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}{\int }_0^1\frac{x^n}{1+x}dx=?$$ Commented by Dwaipayan Shikari last updated on 20/May/21…