Question Number 28885 by abdo imad last updated on 31/Jan/18 $${find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}\:+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{put}\:{I}=\:\int_{−\mathrm{1}}…
Question Number 94418 by niroj last updated on 18/May/20 $$\:\mathrm{1}.\mathrm{F}\boldsymbol{\mathrm{ind}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\theta}\:\mathrm{in}\:\mathrm{Mean}\:\mathrm{Value}\:\mathrm{theorem} \\ $$$$\:\mathrm{f}\left(\mathrm{x}+\mathrm{h}\right)=\:\mathrm{f}\left(\mathrm{x}\right)+\mathrm{hf}^{\:'} \left(\mathrm{x}+\theta\mathrm{h}\right),\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{2}.\mathrm{If}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:\:\:\:+\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\:\:\:=\:\mathrm{k}\left(\mathrm{x}−\mathrm{y}\right)\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}. \\ $$$$\:\mathrm{3}.\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\:\:\:\mathrm{x}^{\mathrm{2}}…
Question Number 28884 by abdo imad last updated on 31/Jan/18 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{cost}\:{ln}\left({tant}\right){dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28882 by abdo imad last updated on 31/Jan/18 $${find}\:\int_{−\pi} ^{\pi} \:\:\:\frac{\mathrm{2}{dt}}{\mathrm{2}+{sint}\:+{cost}}\:. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.\:{e}^{{it}} ={z}…
Question Number 28883 by abdo imad last updated on 31/Jan/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{4}} } \\ $$ Commented by abdo imad last updated on 02/Feb/18…
Question Number 28881 by abdo imad last updated on 31/Jan/18 $${find}\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{2}{t}+\mathrm{2}} \\ $$ Answered by sma3l2996 last updated on 01/Feb/18 $${I}=\int_{−\infty} ^{+\infty}…
Question Number 28879 by abdo imad last updated on 31/Jan/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\frac{{cos}\left({n}\pi{x}\right)}{{n}^{\mathrm{2}} }\:{with}\:\:\mathrm{0}<{x}<\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159931 by qaz last updated on 22/Nov/21 $$\mathrm{Prove}\:::\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}^{\mathrm{m}} }\mathrm{dx}=\frac{\mathrm{1}}{\Gamma\left(\mathrm{m}\right)}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{D}^{\mathrm{m}−\mathrm{1}} \mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{n}+\mathrm{m}\in\mathrm{Odd}\:\mathrm{Number}. \\ $$ Terms of Service…
Question Number 159917 by PengagumRahasiamu last updated on 22/Nov/21 Commented by mr W last updated on 22/Nov/21 $${d}\lfloor{x}\rfloor=\mathrm{0}{dx} \\ $$$$\Rightarrow\int_{{a}} ^{{b}} {f}\left({x}\right){d}\lfloor{x}\rfloor=\int_{{a}} ^{{b}} {f}\left({x}\right)×\mathrm{0}{dx}=\int_{{a}} ^{{b}}…
Question Number 94383 by niroj last updated on 18/May/20 $$\boldsymbol{\mathrm{Integrate}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\int\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{4}} }\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{ii}}\right).\int_{\beta} ^{\:\alpha} \sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\alpha}\right)\left(\beta−\boldsymbol{\mathrm{x}}\right)}\:\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{iii}}\right).\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{y}}/\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}}\:\boldsymbol{\mathrm{dy}}…