Category: Integration

Question Number 137448 by liberty last updated on 03/Apr/21 $${\int }_0^{3/4}\frac{dx}{(x+1)\sqrt{x^2+1}}?$$ Answered by MJS_new last updated on 03/Apr/21 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}= \…

Question Number 137439 by mnjuly1970 last updated on 02/Apr/21 $$\dots \dots nicecalculus\dots ..$$$$provethat::$$$$\mathit{\chi }={\int }_0^1\frac{ln(x+\sqrt{1-x^2})}{x}dx=\frac{{\pi }^2}{16}\dots .$$ Answered by mindispower last updated…

Question Number 137419 by mnjuly1970 last updated on 02/Apr/21 $$\dots \dots \dots mathematical\dots .analysis\dots \dots ..$$$$evaluate\dots .$$$$\mathit{\varphi }={\int }_0^{\mathrm{\infty }}\frac{e^{2\pi x}-e^{\pi x}}{x(1+e^{2\pi x})(1+e^{\pi x})}dx=\lambda {\int }_0^{1}ln(\mathrm{\Gamma }\left(x\right)dx$$$$\:\:\:\:\:\:\:\:\:\:\lambda\:=\:??? \…

Question Number 6333 by FilupSmith last updated on 24/Jun/16 $$I={\int }_0^n\lfloor x\rfloor \lceil x\rceil dx,n\in \mathbb{Z}$$ Commented by nburiburu last updated on 24/Jun/16 $${I}=\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{i}\left({i}+\mathrm{1}\right) \…

Question Number 137397 by mnjuly1970 last updated on 02/Apr/21 $$\dots \dots .\mathcal{A}dvanced\dots \dots \dots \mathcal{C}alculus\dots \dots .$$$$simplify:::$$$${\mathrm{\Omega }}_n=\underset{k=1}{\sum ^{2n+1}}log(1+tan\left(\frac{k\pi }{4(2n+1)}\right))$$$$moreover,findthevalueof::$$$$\mathrm{\Omega }={lim}_{n\to \mathrm{\infty }}\frac{{\mathrm{\Omega }}_n}{n}=???$$…