Category: Integration

Question Number 180780 by universe last updated on 17/Nov/22 Commented by mr W last updated on 20/Nov/22 $$answer\left(a\right)2$$$$seeQ181020$$ Terms of Service…

Question Number 115193 by mnjuly1970 last updated on 24/Sep/20 $$\dots advancedmathematics\dots$$$$::digammalimit::$$$$ifk>0then$$$$provethat$$$$$$$${lim}_{x\to 0}\frac{1}{x}(\psi \left(\frac{k+x}{2x}\right)-\psi \left(\frac{k}{2x}\right))=\frac{1}{k}✓$$$$$$$$\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970}……

Question Number 49645 by maxmathsup by imad last updated on 08/Dec/18 $$calculate\int {\int }_C\mid x+y\mid dxdywithC=[-1,1]\times [-1,1]$$ Answered by ajfour last updated on 08/Dec/18 $${I}\:=\:\mathrm{2}\int_{−\mathrm{1}} ^{\:\:\mathrm{1}} \left[\int_{−{x}}…

Question Number 49635 by maxmathsup by imad last updated on 08/Dec/18 $$1)findf\left(x\right)={\int }_0^{\frac{\pi }{4}}\frac{sint}{2+xcos\left(2t\right)}dt$$$$2)findg\left(x\right)={\int }_0^{\frac{\pi }{4}}\frac{sintsin(2t}{{(2+xcos\left(2t\right))}^2}dx$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{sint}}{\mathrm{2}+\mathrm{3}\:{cos}\left(\mathrm{2}{t}\right)}{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sin}\left({t}\right){sin}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}+\mathrm{3}{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}}…

Question Number 180680 by cortano1 last updated on 15/Nov/22 Answered by ARUNG_Brandon_MBU last updated on 16/Nov/22 $$I={\int }_0^1\frac{x-1+\sqrt{x^2+1}}{x+1+\sqrt{x^2+1}}dx,x=\sinh \theta$$$$\:\:\:=\int_{\mathrm{0}} ^{\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)} \frac{\mathrm{sinh}\theta−\mathrm{1}+\mathrm{cosh}\theta}{\mathrm{sinh}\theta+\mathrm{1}+\mathrm{cosh}\theta}\left(\mathrm{cosh}\theta{d}\theta\right)…