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 $$\:\mathrm{let}\:\mathrm{x}\:=\:\mathrm{100}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{t}\:\Rightarrow\mathrm{dx}=\:\mathrm{200}\:\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:\mathrm{dt} \\ $$$$\:\int_{\mathrm{0}}…
Question Number 127885 by psyche last updated on 02/Jan/21 $$\int\left(\frac{\mathrm{sin}\:\left(\mathrm{2tan}^{−\mathrm{1}} \left({x}\right)+{x}\right)}{{x}}\right)\:\:{the}\:{limit}\:\left[\mathrm{0},\infty\right) \\ $$ Answered by Lordose last updated on 02/Jan/21 $$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{2tan}^{−\mathrm{1}}…
Question Number 62343 by maxmathsup by imad last updated on 20/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left\{{x}\prod_{{k}=\mathrm{1}} ^{\infty} \:{cos}\left(\frac{{x}}{\mathrm{2}^{{k}} }\right)\right\}{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 62342 by maxmathsup by imad last updated on 20/Jun/19 $${let}\:{f}\left(\xi\right)\:=\int\:\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}{dx}\:\:\:{with}\:\:\mathrm{0}<\xi<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{\xi\rightarrow\mathrm{1}} \:\:\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} \theta\:{x}^{\mathrm{2}}…
Question Number 127870 by Eric002 last updated on 02/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2021} \\ $$$${HAPPY}\:{NEW}\:{Year} \\ $$$$\left.\mathrm{1}\right)\int\frac{{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{1}\right)}{dx} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\int\frac{\mathrm{2}{cos}\left({x}\right)−{sin}\left({x}\right)}{\mathrm{3}{sin}\left({x}\right)+\mathrm{5}{cos}\left({x}\right)}{dx} \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\int\frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{6}}…