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}} \\ $$$$ \\ $$$${with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\left(\mathrm{1}+{sin}\theta\:{sinx}\right)^{\mathrm{2}}…
Question Number 78271 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:{A}_{\theta} \:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{2}+{cos}\theta\:{sinx}} \\ $$$$−\pi<\theta<\pi \\ $$ Commented by mathmax by abdo…
Question Number 78270 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$${prove}\:{first}\:{the}\:{convergence}. \\ $$ Commented by mathmax by…
Question Number 78266 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ax}^{\mathrm{3}} \right){dx} \\ $$$${with}\:\mathrm{0}<{a}<\mathrm{1} \\ $$ Commented by mathmax by abdo…
Question Number 78269 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{with} \\ $$$${a}>\mathrm{0}\:\:{find}\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} {f}\left({a}\right){da} \\ $$ Commented by…
Question Number 78264 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\pi} {x}\:{cos}^{\mathrm{4}} {x}\:{dxand}\:{J}=\int_{\mathrm{0}} ^{\pi} {x}\:{sin}^{\mathrm{4}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:{I}\:{and}\:{J} \\ $$…
Question Number 78267 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} −{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax by abdo…