Category: Integration

Question Number 173424 by mnjuly1970 last updated on 11/Jul/22 $$ \\ $$$$\:\:\:\:\mathrm{prove}\:\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{sinh}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\frac{\pi}{\mathrm{2}}\mathrm{tanh}\left(\frac{\pi}{\mathrm{2}}\right) \\ $$$$ \\ $$ Answered by Mathspace…

Question Number 42336 by maxmathsup by imad last updated on 23/Aug/18 $${find}\:\:\int\:{ln}\left({x}−{cosx}\right){dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 107859 by mathmax by abdo last updated on 13/Aug/20 $$\mathrm{find}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{n}} \sqrt{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\left(\mathrm{n}\:\mathrm{natural}\right) \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 42320 by Raj Singh last updated on 23/Aug/18 Commented by Meritguide1234 last updated on 23/Aug/18 Commented by Raj Singh last updated on 24/Aug/18…

Question Number 42305 by maxmathsup by imad last updated on 22/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({xt}\right)}{\left({t}−{i}\right)^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{let}\:{R}\:={Re}\left({f}\left({x}\right)\right)\:{and}\:{I}\:={Im}\left({f}\left({x}\right)\right)\:{extract}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{conclude}\:{the}\:{value}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{t}\right)}{\left({t}−{i}\right)^{\mathrm{2}}…