Question Number 127952 by rs4089 last updated on 03/Jan/21 Answered by Ar Brandon last updated on 03/Jan/21 $$\Psi=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 62416 by mathmax by abdo last updated on 20/Jun/19 $${let}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} {e}^{−{t}} \:{dt}\:\:\:{with}\:{x}>\mathrm{1}\:{calculate}\:\Gamma^{\left({n}\right)} \left({x}\right)\:{for}\:{all}\:{integr}\:{n}. \\ $$ Commented by mathmax by abdo last…
Question Number 62417 by mathmax by abdo last updated on 20/Jun/19 $${prove}\:{that}\:\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:=\frac{\pi}{{sin}\left(\pi{x}\right)}\:\:\:\:\:\:\:{with}\:\mathrm{0}<{x}<\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62414 by mathmax by abdo last updated on 20/Jun/19 $${find}\:\int\:\:\:\:\:\frac{{e}^{{x}} }{\:\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{1}}}{dx} \\ $$ Answered by $@ty@m last updated on 20/Jun/19 $${Put}\:{e}^{{x}} ={t}…
Question Number 62415 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{−{xt}} {ln}\left({yt}\right)\:{dt}\:\:{with}\:{x}>\mathrm{0}\:{and}\:{y}>\mathrm{0}\:. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 127948 by rs4089 last updated on 03/Jan/21 Answered by mathmax by abdo last updated on 04/Jan/21 $$\mathrm{A}_{\mathrm{N}} =\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{\mathrm{2}\pi\mathrm{x}} −\mathrm{1}}{\mathrm{e}^{\mathrm{2}\pi\mathrm{x}} +\mathrm{1}}\left(\frac{\mathrm{1}}{\mathrm{x}}−\frac{\mathrm{x}}{\mathrm{N}^{\mathrm{2}} \:+\mathrm{x}^{\mathrm{2}}…
Question Number 62412 by mathmax by abdo last updated on 20/Jun/19 $${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 62389 by hovea cw last updated on 20/Jun/19 $$\int\mathrm{0dx}= \\ $$$$ \\ $$$$ \\ $$$$\mathrm{help} \\ $$ Commented by mr W last updated…
Question Number 127925 by mr W last updated on 03/Jan/21 $${find}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}+{a}^{\mathrm{2}} {t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt} \\ $$$$ \\ $$$${for}\:{background}\:{see}\:{Q}\mathrm{127811}. \\ $$ Answered by mindispower…
Question Number 127904 by bramlexs22 last updated on 03/Jan/21 $$\:\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\mathrm{100}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}\left(\mathrm{100}−\mathrm{x}\right)}}\:=\:\pi \\ $$ Answered by liberty last updated on 03/Jan/21 $$\:\mathrm{let}\:\mathrm{x}\:=\:\mathrm{100}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{t}\:\Rightarrow\mathrm{dx}=\:\mathrm{200}\:\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:\mathrm{dt} \\ $$$$\:\int_{\mathrm{0}}…