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Author: Tinku Tara

If-a-b-c-d-1-a-2-b-2-c-2-d-2-2-a-3-b-3-c-3-d-3-3-a-4-b-4-c-4-d-4-4-Evaluate-

Question Number 147791 by Tawa11 last updated on 23/Jul/21 $$\mathrm{If}\:\:\:\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:+\:\:\mathrm{c}\:\:+\:\:\mathrm{d}\:\:\:=\:\:\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\mathrm{d}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{3}} \:\:+\:\:\mathrm{b}^{\mathrm{3}} \:\:+\:\:\mathrm{c}^{\mathrm{3}} \:\:+\:\:\mathrm{d}^{\mathrm{3}} \:\:=\:\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{4}} \:\:+\:\:\mathrm{b}^{\mathrm{4}}…

Question-147784

Question Number 147784 by Khalmohmmad last updated on 23/Jul/21 Answered by Olaf_Thorendsen last updated on 23/Jul/21 $${F}\left({x}\right)\:=\:\int\frac{{dx}}{\:\sqrt{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{8}}} \\ $$$${F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}}\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} −\frac{\mathrm{8}}{\mathrm{7}}}} \\ $$$${F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}}\mathrm{argch}\left(\frac{{x}}{\:\sqrt{\frac{\mathrm{8}}{\:\mathrm{7}}}}\right)+\mathrm{C} \\ $$$${F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}}\mathrm{argch}\left(\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{7}}{\mathrm{2}}}{x}\right)+\mathrm{C}…

find-the-function-of-f-when-this-function-continue-at-interval-0-x-2-0-f-t-dt-d-dx-x-1-sin-pix-

Question Number 82244 by M±th+et£s last updated on 19/Feb/20 $${find}\:{the}\:{function}\:{of}\:{f}\:{when}\:{this}\:\: \\ $$$${function}\:{continue}\:{at}\:{interval}\:\left[−\infty,\mathrm{0}\right] \\ $$$$\int_{−{x}^{\mathrm{2}} } ^{\mathrm{0}} {f}\left({t}\right)\:{dt}=\frac{{d}}{{dx}}\left[{x}\left(\mathrm{1}−{sin}\left(\pi{x}\right)\right]\right. \\ $$ Commented by mr W last updated…

find-the-solution-x-sin-y-x-dy-y-sin-y-x-x-dx-

Question Number 82245 by jagoll last updated on 19/Feb/20 $${find}\:{the}\:{solution}\: \\ $$$${x}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:{dy}\:=\:\left[{y}\:\mathrm{sin}\:\left(\frac{{y}}{{x}}\right)\:−{x}\right]\:{dx} \\ $$ Commented by john santu last updated on 19/Feb/20 $${let}\:{v}\:=\:\frac{{y}}{{x}}\:\Rightarrow\:{y}\:=\:{vx} \\ $$$$\frac{{dy}}{{dx}}\:=\:{v}\:+\:\frac{{dv}}{{dx}}\:\Rightarrow\:{dy}\:={v}\:{dx}+\:{dv}\:…