Question Number 61978 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{t}^{\mathrm{3}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 61979 by maxmathsup by imad last updated on 13/Jun/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 13/Jun/19…
Question Number 61976 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{A}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{dxdy}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\…
Question Number 193036 by ali009 last updated on 02/Jun/23 $${if}\:{f}\left({x}\right)={x}\sqrt{\left(\mathrm{16}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$${find}\:\int_{\mathrm{0}.\mathrm{5}} ^{\mathrm{3}.\mathrm{5}} {f}\left({x}\right)\:{dx}\:{using}\:{trapezoidal}\:{method} \\ $$$${then}\:{find}\:{the}\:{max}\:{and}\:{min}\:{value}\:{of}\:{the}\:{error} \\ $$$$\:{with}\:{the}\:{given}\:{n}\:{steps} \\ $$$${x}_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}_{{n}} \right) \\…
Question Number 61966 by aliesam last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −{e}^{−\mathrm{2}{x}} }\:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} }}{dx}=\int\frac{{e}^{\mathrm{2}{x}} }{{e}^{\mathrm{2}{x}}…
Question Number 127495 by mnjuly1970 last updated on 30/Dec/20 Answered by panky0214 last updated on 01/Jan/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127468 by bramlexs22 last updated on 30/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{x}^{\mathrm{3}} \:\mathrm{sin}\:\left(\lambda\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\:\mathrm{dx}\:=?\: \\ $$ Commented by bramlexs22 last updated on 30/Dec/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:\mathrm{sir} \\…
Question Number 127464 by bramlexs22 last updated on 30/Dec/20 Answered by liberty last updated on 30/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61921 by maxmathsup by imad last updated on 11/Jun/19 $${let}\:{A}\:=\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} \:−\mathrm{2}{i}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{extract}\:{Re}\left({A}\right)\:{and}\:{Im}\left({A}\right)\:{and}\:{determine}\:{its}\:{values}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$ Commented by…
Question Number 127446 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:…{challanging}\:\:{integral}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \left({cos}\left({x}\right)−\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} \:}\right)\frac{{dx}}{{x}}\:=\:−\gamma\:\: \\ $$$$ \\ $$ Answered by mindispower last…