Category: Integration

Question Number 183109 by cortano1 last updated on 20/Dec/22 $$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt{\mathrm{sin}\:{x}+\mathrm{1}}}{\:\sqrt{\mathrm{cos}\:{x}+\mathrm{1}}}\:{dx}\:=?\: \\ $$ Answered by universe last updated on 20/Dec/22 $$ \\ $$$$\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…

Question Number 51997 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dt}}{\mathrm{1}+{xsint}}\:\:{with}\:{x}>−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({o}\right)\:,{f}\left(\mathrm{1}\right)\:{and}\:{f}\left(\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{give}\:{f}\:{at}\:{form}\:{of}\:{function}\: \\ $$$$ \\ $$ Commented by maxmathsup…

Question Number 51994 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{D}_{{n}} =\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:\:/\left({x},{y}\right)\in\left[\frac{\mathrm{1}}{{n}}\:,{n}\left[\:\right\}\right.\right. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int\int_{{D}_{{n}} } \:\:\:\:\:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:{e}^{−{x}^{\mathrm{2}}…

Question Number 51991 by maxmathsup by imad last updated on 01/Jan/19 $${find}\:{f}\left({a}\right)\:=\int\:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{ax}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{ax}^{\mathrm{2}} }}\:\:{with}\:{a}>\mathrm{0} \\ $$ Commented by Abdo msup. last updated on 05/Jan/19 $${changement}\:{x}\sqrt{{a}}={t}\:{give}…

Question Number 51990 by maxmathsup by imad last updated on 01/Jan/19 $${calculate}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:{x}\:{arctan}\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$ Answered by peter frank last updated on 01/Jan/19…