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}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\int\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{4}} }\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{ii}}\right).\int_{\beta} ^{\:\alpha} \sqrt{\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\alpha}\right)\left(\beta−\boldsymbol{\mathrm{x}}\right)}\:\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\left(\boldsymbol{\mathrm{iii}}\right).\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{y}}/\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}}\:\boldsymbol{\mathrm{dy}}…
Question Number 159915 by tounghoungko last updated on 22/Nov/21 $$\:\:\int_{\mathrm{1}} ^{\mathrm{16}} \:\frac{\sqrt{{x}}}{\mathrm{1}+\sqrt[{\mathrm{4}}]{{x}^{\mathrm{3}} }}\:{dx}\:=? \\ $$ Commented by blackmamba last updated on 22/Nov/21 $$\:\:\:{let}\:\sqrt[{\mathrm{4}}]{{x}}\:=\:{v}\:\Rightarrow\begin{cases}{{v}_{\mathrm{1}} =\mathrm{1}}\\{{v}_{\mathrm{2}} =\mathrm{2}}\end{cases}\:\Rightarrow{x}={v}^{\mathrm{4}}…
Question Number 28833 by abdo imad last updated on 30/Jan/18 $${let}\:{give}\:\varphi\left({x}\right)\:={x}\:,\varphi\:\mathrm{2}\pi\:{periodique}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series}\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} }\:{and}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$ Terms…
Question Number 28830 by abdo imad last updated on 30/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:{ch}\left(\alpha{x}\right)\:{and}\:\mathrm{2}\pi\:{periodic}\:{with}\:\alpha\neq\mathrm{0} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28832 by abdo imad last updated on 30/Jan/18 $${find}\:{the}\:{value}\:{of}\:\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{{n}+\mathrm{1}} \sqrt{{t}−\mathrm{1}}}\:.{withn}\in{N}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com