Question Number 63251 by Tawa1 last updated on 01/Jul/19 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{m}\:\mathrm{cos}\theta\right)\:\mathrm{d}\theta \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128775 by bramlexs22 last updated on 10/Jan/21 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{let}\:\varphi\:=\:\sqrt{\frac{\mathrm{1}+\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\Rightarrow\mathrm{x}\:=\:\frac{\varphi^{\mathrm{2}} −\mathrm{1}}{\varphi^{\mathrm{2}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{dx}\:=\:\frac{\mathrm{4}\varphi}{\left(\varphi^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}}…
Question Number 63232 by mathmax by abdo last updated on 01/Jul/19 $${let}\:{B}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}\right)^{{x}−\mathrm{1}} {t}^{{y}−\mathrm{1}} \:{dt} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{convergence}\:{of}\:{B}\left({x},{y}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{B}\left({x},{y}\right)={B}\left({y},{x}\right) \\ $$$${prove}\:{that}\:{B}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{x}−\mathrm{1}} }{\left(\mathrm{1}+{t}\right)^{{x}+{y}}…
Question Number 128750 by bemath last updated on 10/Jan/21 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\:\mathrm{satisfy}\:\mathrm{f}\left(−\mathrm{x}\right)=\mathrm{3f}\left(\mathrm{x}\right). \\ $$$$\mathrm{If}\:\int_{−\mathrm{1}} ^{\:\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{2}\:\mathrm{then}\:\int_{−\mathrm{2}} ^{\:\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=? \\ $$ Commented by mr W last updated on…
Question Number 63214 by mathmax by abdo last updated on 30/Jun/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{x}\:{e}^{−\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }} \:\:{sin}\left({bx}\right){dx}\:\:{with}\:\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 128736 by mnjuly1970 last updated on 09/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:{evluate}\::: \\ $$$$\:\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}^{\mathrm{2}} } {cos}\left({x}\right){dx}=? \\ $$$$ \\ $$ Commented…
Question Number 128721 by rs4089 last updated on 09/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\:\mathrm{x}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 09/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 128710 by rs4089 last updated on 09/Jan/21 $$\int{e}^{{x}} \left(\frac{\mathrm{1}+{sinx}+{cosx}}{{cos}^{\mathrm{2}} {x}}\right)\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128707 by mnjuly1970 last updated on 09/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{nice}\:\:\mathrm{calculus}… \\ $$$${prove}\:\:{that}::\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+\varphi^{\mathrm{2}} {x}^{\mathrm{2}} \right)}{\mathrm{1}+\pi^{\mathrm{2}} {x}^{\mathrm{2}} }\:{dx}={ln}\left(\frac{\pi+\varphi}{\pi}\right) \\ $$$$\varphi::=\:\:{golen}\:{ratio}… \\ $$$$ \\…
Question Number 128702 by bemath last updated on 09/Jan/21 $$\:\mathrm{If}\:\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{3}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\mathrm{then}\: \\ $$$$\:\frac{\mathrm{sin}\:^{\mathrm{8}} \mathrm{x}}{\mathrm{8}}\:+\:\frac{\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}}{\mathrm{27}}\:=\:? \\ $$ Answered by liberty last updated on 09/Jan/21…