Category: Differentiation

Question Number 61675 by peter frank last updated on 06/Jun/19 Commented by peter frank last updated on 06/Jun/19 $$findsolutionofD.E$$ Answered by ajfour last…

Question Number 127119 by liberty last updated on 27/Dec/20 $$Thebarometricpressurepatanaltitude$$$$ofhmilesabovesealevelsatisfiesthe$$$$differentialequation\frac{dp}{dh}=-0.2p.$$$$Ifthepressureatsealevelis29.92inches$$$$ofmercury,findthebarometric$$$$preassureat17,000ft$$$$\left(A\right)56.97in\left(B\right)15.71in$$$$\left({C}\right)\:\mathrm{7}.\mathrm{86}\:{in}\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{1}\:{in} \…

Question Number 192545 by peter frank last updated on 20/May/23 Answered by BaliramKumar last updated on 20/May/23 $$\mathrm{plnx}+\mathrm{qlny}=(\mathrm{p}+\mathrm{q})\ln (\mathrm{x}+\mathrm{y})$$$$\frac{\mathrm{p}}{\mathrm{x}}-\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}=\{\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}-\frac{\mathrm{q}}{\mathrm{y}}\}\frac{\mathrm{dy}}{\mathrm{dx}}$$$$\frac{\mathrm{py}}{\mathrm{x}}\frac{-\mathrm{qx}}{}=\left\{\frac{\mathrm{py}-}{}\frac{\mathrm{qx}}{\mathrm{y}}\right\}\frac{\mathrm{dy}}{\mathrm{dx}}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}}{\mathrm{x}} \…

Question Number 126994 by bramlexs22 last updated on 26/Dec/20 $$\int \frac{x^4}{1+x^8}dx=?$$ Answered by liberty last updated on 26/Dec/20 $$\Omega=\int\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:=\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}}…

Question Number 126971 by mnjuly1970 last updated on 25/Dec/20 $$\dots nicecalculus\dots$$$$evaluate{}^{\prime }:$$$$\mathrm{\Omega }={\int }_0^1{\left(arctan\left(x\right)\right)}^{2}dx=?$$$$$$ Answered by Dwaipayan Shikari…