Question Number 169706 by MikeH last updated on 06/May/22 $$\mathrm{using}\:\mathrm{cylindrical}\:\mathrm{coordinates}\:\begin{cases}{{x}={r}\mathrm{cos}\theta}\\{{y}\:=\:{r}\mathrm{sin}\:\theta}\\{{z}={z}}\end{cases} \\ $$$$\mathrm{to}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{integral} \\ $$$${K}=\:\int\int\int_{{S}} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} }\:{dxdydz} \\ $$$$\mathrm{where} \\ $$$$\:{S}=\:\left\{\left({x},{y},{z}\right)\:\in\mathbb{R}^{\mathrm{3}} :\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\leqslant\:\mathrm{4},\:\mathrm{0}\:\leqslant{z}\leqslant\sqrt{{x}^{\mathrm{2}}…
Question Number 169677 by cortano1 last updated on 06/May/22 $$\:\:\:\:{M}\:=\:\int\:\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{8}}}\:=? \\ $$ Answered by MJS_new last updated on 06/May/22 $$\int\frac{{dx}}{\left({x}+{c}\right)\sqrt{{x}^{\mathrm{2}} +{ax}+{b}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}^{\mathrm{2}} +{ax}+{b}}+{x}+\frac{{a}}{\mathrm{2}}\:\rightarrow\:{dx}=\frac{\sqrt{{x}^{\mathrm{2}}…
Question Number 169654 by CrispyXYZ last updated on 05/May/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:\mathrm{d}{x}\:=\:? \\ $$ Answered by floor(10²Eta[1]) last updated on 05/May/22 $$\sqrt{\mathrm{x}^{\mathrm{2}}…
Question Number 104104 by bemath last updated on 19/Jul/20 $$\int\:\frac{{x}\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx}\:? \\ $$ Answered by OlafThorendsen last updated on 19/Jul/20 $$\mathrm{By}\:\mathrm{parts}\:: \\ $$$$\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\mathrm{arctan}{x}−\int\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 38536 by gunawan last updated on 27/Jun/18 $$\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{\:\sqrt{\mathrm{3}−\mathrm{cos}\:{x}}}= \\ $$ Answered by MJS last updated on 27/Jun/18 $$\approx\mathrm{1}.\mathrm{85407} \\ $$ Answered…
Question Number 38516 by rahul 19 last updated on 26/Jun/18 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mid\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\mid\mathrm{d}{x} \\ $$ Commented by math khazana by abdo last updated on 27/Jun/18…
Question Number 104028 by mathmax by abdo last updated on 19/Jul/20 $$\mathrm{calculate}\:\:\int_{\mathrm{20}} ^{+\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{18}\right)^{\mathrm{19}} \left(\mathrm{x}−\mathrm{19}\right)^{\mathrm{18}} } \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 169563 by cortano1 last updated on 03/May/22 Commented by infinityaction last updated on 03/May/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 169559 by TOTTI last updated on 03/May/22 Commented by cortano1 last updated on 03/May/22 $$\:\mathrm{2}^{{nd}} \:{way}\: \\ $$$$\:\:\begin{array}{|c|c|c|}{{x}}&\hline{\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\\{\mathrm{1}}&\hline{−\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\\{\mathrm{0}}&\hline{−\frac{\mathrm{4}}{\mathrm{15}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} }\\\hline\end{array} \\ $$$$\:{I}=\int\:{x}\:\sqrt{\mathrm{1}−{x}}\:{dx}\:=\:−\frac{\mathrm{2}}{\mathrm{3}}{x}\:\sqrt{\left(\mathrm{1}−{x}\right)^{\mathrm{3}}…
Question Number 169548 by mathlove last updated on 02/May/22 Commented by infinityaction last updated on 02/May/22 $$\int\frac{{x}}{\mathrm{2cos}\:^{\mathrm{2}} {x}/\mathrm{2}}{dx}\:+\:\int\frac{\mathrm{2sin}\:{x}/\mathrm{2}\:\mathrm{cos}\:{x}/\mathrm{2}}{\mathrm{2cos}\:^{\mathrm{2}} {x}/\mathrm{2}}{dx} \\ $$$$\underset{{by}\:{parts}\:} {\underbrace{\frac{\mathrm{1}}{\mathrm{2}}\int{x}\mathrm{sec}\:^{\mathrm{2}} {x}/\mathrm{2}\:{dx}}}\:+\:\int\mathrm{tan}\:{x}/\mathrm{2}\:{dx} \\ $$$${be}\:{continued}…