Question Number 78284 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:\int\int_{{D}} {xy}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} }{dxdy} \\ $$$${D}=\left\{\left({x},{y}\right)/\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right\} \\ $$ Commented by abdomathmax last…
Question Number 78283 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:\int\int_{{D}} \:\left({x}^{\mathrm{2}} +\mathrm{2}{y}\right){dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \geqslant{y}\:{and}\:{y}\geqslant{x}^{\mathrm{2}} \right\} \\ $$ Commented by mr…
Question Number 12744 by tawa last updated on 30/Apr/17 $$\int_{\:\mathrm{e}^{−\mathrm{3}} } ^{\:\mathrm{e}^{−\mathrm{2}} } \:\:\frac{\mathrm{1}}{\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{x}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $${logx}={t}\Rightarrow{dx}/{x}={dt} \\…
Question Number 78281 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:\:\int\int_{{W}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} }{{e}^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } }{dxdy} \\ $$$${with}\:{W}\:=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$ Terms of…
Question Number 78276 by msup trace by abdo last updated on 15/Jan/20 $${find}\:{I}_{{n}} =\int\int_{\left[\mathrm{1},{n}\right]^{\mathrm{2}} } \:\:\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{ln}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy} \\ $$ Commented by mathmax…
Question Number 12742 by Joel577 last updated on 30/Apr/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\:\frac{{dx}}{\left({x}\:+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\mathrm{2}}}\:=\:\frac{−\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{2}}}{{x}\:+\:\mathrm{1}}\:+\:{C} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $$\frac{\mathrm{1}}{{x}+\mathrm{1}}={t}\Rightarrow\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 78277 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:\int\int_{{W}} \:\:\:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }+\mathrm{3}}{dxdy} \\ $$$${with}\:{W}\:=\left\{\:\left({x},{y}\right)/\:{x}>\mathrm{0}\:{and}\:{y}>\mathrm{0}\right\} \\ $$ Terms of…
Question Number 143808 by mnjuly1970 last updated on 18/Jun/21 Answered by Dwaipayan Shikari last updated on 18/Jun/21 $$\xi\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{{a}} \right)^{{a}} }{dx} \\ $$$$=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}} ^{\infty}…
Question Number 12740 by malwaan last updated on 30/Apr/17 $$\int\mid\mathrm{x}\mid\:\mathrm{dx} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $$\mid{x}\mid=\begin{cases}{{x}\:\:{if}\:\:{x}\geqslant\mathrm{0}.}\\{−{x}\:{if}\:\:{x}<\mathrm{0}}\end{cases} \\ $$$${I}=\left(\int{xdx}\right)\:{or}\left(\int−{xdx}\right)=\left(\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right){or}\left(\frac{−{x}^{\mathrm{2}} }{\mathrm{2}}\right)+\boldsymbol{{C}} \\…
Question Number 78273 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{f}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\mathrm{1}+{sin}\theta\:{sinx}} \\ $$$$ \\ $$$${with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\left(\mathrm{1}+{sin}\theta\:{sinx}\right)^{\mathrm{2}}…