Category: Integration

Question Number 62420 by mathsolverby Abdo last updated on 20/Jun/19 $$let{u}_n\left(x\right)=\frac{1}{n^x}-{\int }_n^{n+1}\frac{dt}{t^x}withx\in [1,2]$$$$1)provethat0⩽u_n\left(x\right)⩽\frac{1}{n^x}-\frac{1}{{(n+1)}^x}(n>0)$$$$\left.\mathrm{2}\right){prove}\:{that}\:\Sigma\:{u}_{{n}} \left({x}\right){converges} \…

Question Number 62418 by mathmax by abdo last updated on 20/Jun/19 $$calculate{\int }_0^1\mathrm{\Gamma }\left(t\right).\mathrm{\Gamma }(1-t)dt$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 127952 by rs4089 last updated on 03/Jan/21 Answered by Ar Brandon last updated on 03/Jan/21 $$\Psi=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\frac{\mathrm{x}^{\mathrm{2}}…

Question Number 62417 by mathmax by abdo last updated on 20/Jun/19 $$provethat\mathrm{\Gamma }\left(x\right).\mathrm{\Gamma }(1-x)=\frac{\pi }{sin\left(\pi x\right)}with0<x<1$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 62415 by mathmax by abdo last updated on 20/Jun/19 $$calculatef(x,y)={\int }_0^{\mathrm{\infty }}{e}^{-xt}ln\left(yt\right)dtwithx>0andy>0.$$ Commented by mathmax by abdo last updated on…