Question Number 30566 by abdo imad last updated on 23/Feb/18 $${study}\:{the}\:{convergence}\:{of}\:{A}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{\alpha−\mathrm{1}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and} \\ $$$${find}\:{its}\:{value}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30568 by abdo imad last updated on 23/Feb/18 $${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30564 by abdo imad last updated on 23/Feb/18 $${f}\:{and}\:{g}\:{are}\:\mathrm{2}\:{function}\:\:{C}^{{n}} \:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\int_{{a}} ^{{b}} \:{f}^{\left({n}\right)} \left({x}\right){g}\left({x}\right){dx}=\left[\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(−\mathrm{1}\right)^{{k}} \:{f}^{\left({k}\right)} {g}^{\left({n}−{k}\right)} \right]_{{a}} ^{{b}} \:+\left(−\mathrm{1}\right)^{{n}} \int_{{a}}…
Question Number 96097 by mhmd last updated on 29/May/20 Answered by mathmax by abdo last updated on 29/May/20 $$\mathrm{A}\:=\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\left(\mathrm{e}^{\mathrm{x}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)}\:\mathrm{changement}\:\mathrm{x}=−\mathrm{t}\:\mathrm{give} \\ $$$$\mathrm{A}\:=−\int_{−\mathrm{1}}…
Question Number 30559 by abdo imad last updated on 23/Feb/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{{n}} {dt}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96092 by mhmd last updated on 29/May/20 $${find}\:\int\frac{{dx}}{{tan}^{−\mathrm{1}} \left({x}\right)} \\ $$ Commented by bemath last updated on 30/May/20 $$\int\:\mathrm{cot}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\:\mathrm{I} \\ $$$$\mathrm{by}\:\mathrm{parts}\:.\:\mathrm{u}\:=\:\mathrm{cot}^{−\mathrm{1}} \left({x}\right)\Rightarrow{du}=−\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 30557 by abdo imad last updated on 23/Feb/18 $${if}\:\varphi\:{convexe}\:{and}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\varphi\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}\left({t}\right){dt}\right)\leqslant\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:\varphi{of}\left({t}\right){dt}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30554 by abdo imad last updated on 23/Feb/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{xcos}\theta\:+\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{2}{xcos}\theta\:+\mathrm{1}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30555 by abdo imad last updated on 23/Feb/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{4}} }}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30548 by abdo imad last updated on 23/Feb/18 $${let}\:{put}\:\:{for}\:\mid\lambda\mid<\mathrm{1}\:\:\:\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{cos}\left({nx}\right)}{\mathrm{1}−\mathrm{2}\lambda{cosx}\:+\lambda^{\mathrm{2}} }{dx}\: \\ $$$${find}\:{u}_{{n}} \:{interms}\:{of}\:{n}\:{and}\:\lambda. \\ $$ Terms of Service Privacy Policy…