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Category: Integration

I-For-witch-value-of-the-integral-C-0-1-1-2x-2-1-x-1-dx-conveege-And-in-this-case-calculate-II-Let-x-y-x-y-2-a-Calculate-I-1-dxdy-and-

Question Number 79730 by Henri Boucatchou last updated on 27/Jan/20 $$\left.{I}\right)\:\:{For}\:{witch}\:{value}\:{of}\:\alpha\:{the}\:{integral} \\ $$$$\:{C}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\mathrm{1}}{{x}+\mathrm{1}}\right){dx}\:\:{conveege}\:\:? \\ $$$${And}\:{in}\:{this}\:{case}\:{calculate}\:\alpha. \\ $$$$\left.{II}\right)\:\:{Let}\:\Delta=\left\{\left({x};\:{y}\right)/\:\mid{x}\mid+\mid{y}\mid\leqslant\mathrm{2}\right\} \\ $$$$\left.\:\:\:\:\:{a}\right)\:{Calculate}\:{I}_{\mathrm{1}} =\:\int\int_{\Delta} {dxdy}\:\:\:{and}\:\:\int\int_{\Delta} \frac{{dxdy}}{\left(\mid{x}\mid+\mid{y}\mid\right)^{\mathrm{2}}…

Calculus-I-n-1-Arccot-3-n-n-1-3-

Question Number 145270 by mnjuly1970 last updated on 03/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:#\:\mathrm{Calculus}\:\left(\:\mathrm{I}\:\right)\:# \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{Arccot}\left(\mathrm{3}\:+\frac{{n}\:\left(\:{n}\:+\:\mathrm{1}\right)}{\mathrm{3}}\:\right)=\:? \\ $$$$\:\:\:\:\:\:….. \\ $$ Answered by Olaf_Thorendsen last updated…

sec-6-x-dx-

Question Number 14181 by tawa tawa last updated on 29/May/17 $$\int\:\mathrm{sec}^{\mathrm{6}} \left(\mathrm{x}\right)\:\:\mathrm{dx}\:\: \\ $$ Answered by ajfour last updated on 29/May/17 $${let}\:\mathrm{tan}\:{x}={t} \\ $$$$\Rightarrow\mathrm{sec}\:^{\mathrm{2}} {xdx}={dt},\:{and}\:{we}\:{know}…

evaluate-n-0-1-n-n-4-n-2-1-e-2-

Question Number 145200 by qaz last updated on 03/Jul/21 $$\mathrm{evaluate}::\:\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}!\left(\mathrm{n}^{\mathrm{4}} +\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}=\frac{\mathrm{e}}{\mathrm{2}} \\ $$ Answered by mindispower last updated on 03/Jul/21 $${n}^{\mathrm{4}} +{n}^{\mathrm{2}}…

Question-79634

Question Number 79634 by TawaTawa last updated on 26/Jan/20 Commented by mathmax by abdo last updated on 27/Jan/20 $$\Omega\:=\int_{\frac{\pi}{\mathrm{5}}} ^{\frac{\mathrm{3}\pi}{\mathrm{10}}} \:\frac{{x}}{{sin}\left(\mathrm{2}{x}\right)}{dx}\:\:{changement}\:{x}=\frac{\pi}{\mathrm{2}}−{t}\:{givet}=\frac{\pi}{\mathrm{2}}−{x} \\ $$$$\Omega=\int_{\frac{\mathrm{3}\pi}{\mathrm{10}}} ^{\frac{\pi}{\mathrm{5}}} \:\frac{\frac{\pi}{\mathrm{2}}−{t}}{{sin}\left(\mathrm{2}{t}\right)}\left(−{dt}\right)\:=\frac{\pi}{\mathrm{2}}\int_{\frac{\pi}{\mathrm{5}}}…