Question Number 65768 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 65771 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\…
Question Number 65767 by mathmax by abdo last updated on 03/Aug/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{4}} +{x}^{\mathrm{4}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }…
Question Number 65763 by 9325328488 last updated on 03/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221 by 123456 last updated on 25/Jan/15 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\mathrm{tan}\:{x}\:\mathrm{arctan}\:{x}\:{dx} \\…
Question Number 216 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate} \\ $$$$\underset{−\infty} {\overset{+\infty} {\int}}{f}\left({x}\right){dx} \\ $$$$\mathrm{where} \\ $$$${f}\left({x}\right)=\begin{cases}{{e}^{{x}} }&{{x}\leqslant\mathrm{0}}\\{\mathrm{1}+{x}}&{\mathrm{0}<{x}\leqslant\mathrm{1}}\\{\mathrm{1}+{x}^{\mathrm{2}} }&{\mathrm{1}<{x}\leqslant\mathrm{2}}\\{\mathrm{5}}&{\mathrm{2}<{x}\leqslant\mathrm{5}}\\{\frac{\mathrm{5}}{\mathrm{1}+\left({x}−\mathrm{5}\right)^{\mathrm{2}} }}&{{x}>\mathrm{5}}\end{cases} \\ $$ Answered by…
Question Number 131286 by mnjuly1970 last updated on 03/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:{find}\:::\:\:{i}::\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} −\mathrm{1}}\right)=? \\ $$$$\:\:\:\: \\…
Question Number 65740 by rajesh4661kumar@gmail.com last updated on 03/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{\frac{\mathrm{1}}{{cosx}}\:+{sinx}}\:\Rightarrow\:{A}\:=\int\:\frac{{cosx}}{\mathrm{1}+{cosx}\:{sinx}}{dx}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}\:}\right)\:={t}\:{give}\:{A}\:=\int\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 65736 by malwaan last updated on 03/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}\:+\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:? \\ $$ Commented by Souvik Ghosh last updated on 03/Aug/19 $${let}\:\:\:{u}=\mathrm{2}{x}\Leftrightarrow{du}=\mathrm{2}{dx} \\…
Question Number 191 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:\underset{\mathrm{C}} {\int}\frac{{z}^{\mathrm{2}} \mathrm{sin}\:{z}\:\mathrm{cos}\:{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)\left({z}^{\mathrm{2}} −\mathrm{1}\right)}{dz}\: \\ $$$$\mathrm{where}\:\mathrm{C}=\left\{{z}\in\mathbb{C}\mid\mid{z}\mid=\mathrm{2}\right\} \\ $$ Answered by nileshkulkarni last updated on 15/Dec/14…