Question Number 133214 by mathmax by abdo last updated on 20/Feb/21 $$\mathrm{calculate}\:\mathrm{f}\left(\xi\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}\:\mathrm{sin}\left(\xi\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133213 by mathmax by abdo last updated on 20/Feb/21 $$\mathrm{calculate}\:\mathrm{c}\left(\xi\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\xi\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 67674 by Abdo msup. last updated on 30/Aug/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +{a}\right)}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{a}\right)^{\mathrm{2}} } \\…
Question Number 67673 by Abdo msup. last updated on 30/Aug/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)} \\ $$ Commented by Abdo msup. last updated on 30/Aug/19…
Question Number 133187 by mnjuly1970 last updated on 19/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{CALCULUS}…… \\ $$$$\:\:\:\:\:{lim}\:_{{n}\rightarrow\infty} \left({n}\left({ln}\left(\mathrm{2}\right)−\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}}\right)\right)=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 2103 by Yozzi last updated on 02/Nov/15 $${Find}\:{the}\:{integral} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}. \\ $$ Commented by Yozzi last updated on 02/Nov/15 $${Yup}. \\…
Question Number 133173 by john_santu last updated on 19/Feb/21 $$\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 19/Feb/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 67628 by mhmd last updated on 29/Aug/19 $$\int{x}^{{n}} {lnx}/{n}^{{x}\:} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2088 by Yozzi last updated on 01/Nov/15 $${Show}\:{that}\:\forall{n}\in\mathbb{Z}^{+} \\ $$$$\int_{\mathrm{0}} ^{\pi/\mathrm{4}} {tan}^{\mathrm{2}{n}+\mathrm{1}} \theta{d}\theta=\left(−\mathrm{1}\right)^{{n}} \left(\frac{\mathrm{1}}{\mathrm{2}}{ln}\mathrm{2}+\underset{{m}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}} }{\mathrm{2}{m}}\right). \\ $$$${Deduce}\:{that}\:\underset{\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}−\mathrm{1}} }{\mathrm{2}{m}}=\mathrm{0}.\mathrm{5}{ln}\mathrm{2}. \\…
Question Number 2089 by Yozzi last updated on 01/Nov/15 $${If}\:{x}\in\left[\mathrm{0},\mathrm{0}.\mathrm{5}\pi\right],\:{show}\:{that}\:{sinx}\geqslant{x}−\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} . \\ $$$${Hence}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{3000}}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{10}} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}+{sinx}\right)^{\mathrm{2}} }{dx}\leqslant\frac{\mathrm{2}}{\mathrm{5999}}. \\ $$ Commented by prakash jain…