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Category: Integration

Determine-the-fourth-roots-of-16-giving-the-results-in-the-form-a-jb-

Question Number 14588 by tawa tawa last updated on 02/Jun/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{roots}\:\mathrm{of}\:\:\:−\:\mathrm{16},\:\:\:\mathrm{giving}\:\mathrm{the}\:\mathrm{results}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\:\mathrm{a}\:+\:\mathrm{jb}. \\ $$ Answered by mrW1 last updated on 03/Jun/17 $${z}^{\mathrm{4}} =−\mathrm{16} \\ $$$${z}={x}+{iy}={r}\left(\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta\right) \\…

Find-the-arc-lenght-of-the-function-y-2-x-3-a-where-a-is-a-constant-for-0-x-7a-3-

Question Number 145646 by physicstutes last updated on 06/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{y}^{\mathrm{2}} \:=\:\frac{{x}^{\mathrm{3}} }{{a}}\:\mathrm{where}\:{a}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{for} \\ $$$$\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{7}{a}}{\mathrm{3}} \\ $$ Answered by Olaf_Thorendsen last updated on 06/Jul/21 $${y}^{\mathrm{2}} \:=\:\frac{{x}^{\mathrm{3}}…

Question-14523

Question Number 14523 by 1kanika# last updated on 01/Jun/17 Answered by linkelly0615 last updated on 01/Jun/17 $${set}\:{dV}={dxdydz} \\ $$$${Origin}=\int\int\int_{\left[\mathrm{0},\mathrm{1}\right)^{\mathrm{3}} } \left(\mathrm{0}+\mathrm{0}+\mathrm{0}\right){dV}=\mathrm{0} \\ $$ Commented by…

Question-145588

Question Number 145588 by naka3546 last updated on 06/Jul/21 Answered by chengulapetrom last updated on 06/Jul/21 $${let}\:\mathrm{2}{sec}\theta={x} \\ $$$$\mathrm{2}{sec}\theta{tan}\theta{d}\theta={dx} \\ $$$$=\mathrm{2}\int\frac{\mathrm{2}{tan}^{\mathrm{2}} \theta{sec}\theta}{\mathrm{2}{sec}\theta}{d}\theta \\ $$$$=\mathrm{2}\int{tan}^{\mathrm{2}} \theta{d}\theta…