Category: None

Question Number 127211 by mohammad17 last updated on 27/Dec/20 $$\int_{\mathrm{0}} ^{\:\pi^{\mathrm{2}} } {x}^{−\frac{\mathrm{1}}{\mathrm{2}}} {e}^{−{x}} {dx} \\ $$ Answered by Dwaipayan Shikari last updated on 27/Dec/20…

Question Number 127203 by naka3546 last updated on 27/Dec/20 $$\int\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{26}}}\:\:=\:\:\centerdot\centerdot\centerdot\:\:? \\ $$$${Please}\:\:{show}\:\:{your}\:\:{workings}\:\:! \\ $$ Commented by liberty last updated on 27/Dec/20 $$\:\int\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} }}\:…

Question Number 192732 by mokys last updated on 25/May/23 $${let}\:{the}\:{closed}\:{interval}\:\left[{a},{b}\right]\:{be}\:{the}\:{domain}\:{of}\:{the}\:{function}\:{f}\: \\ $$$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}−\mathrm{3}\right)\:{and}\:{f}\left({x}+\mathrm{3}\right)\:?\:\: \\ $$ Answered by MM42 last updated on 25/May/23 $${a}\leqslant{x}−\mathrm{3}\leqslant{b}\Rightarrow{a}+\mathrm{3}\leqslant{x}\leqslant{b}+\mathrm{3}\Rightarrow{D}_{{f}−\mathrm{3}} =\left[{a}+\mathrm{3},{b}+\mathrm{3}\right] \\ $$$${a}\leqslant{x}+\mathrm{3}\leqslant{b}\Rightarrow{a}−\mathrm{3}\leqslant{x}\leqslant{b}−\mathrm{3}\Rightarrow{D}_{{f}+\mathrm{3}}…

Question Number 127182 by danielasebhofoh last updated on 27/Dec/20 Answered by Dwaipayan Shikari last updated on 27/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{\frac{{i}\pi{x}}{\mathrm{2}}} {dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{i}^{{x}} ={e}^{\frac{{i}\pi{x}}{\mathrm{2}}} \\ $$$$=\frac{\mathrm{2}}{\pi{i}}\left({e}^{\frac{{i}\pi}{\mathrm{2}}} −\mathrm{1}\right)=\frac{\mathrm{2}}{\pi{i}}\left({i}−\mathrm{1}\right)=\frac{\mathrm{2}}{\pi}−\frac{\mathrm{2}}{\pi{i}}=\frac{\mathrm{2}}{\pi}\left(\mathrm{1}+{i}\right)…

Question Number 127158 by Jamshidbek last updated on 27/Dec/20 Commented by mr W last updated on 27/Dec/20 $${x}=\phi={golden}\:{ratio}\approx\mathrm{1}.\mathrm{618} \\ $$ Answered by mindispower last updated…