Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 104071 by DGmichael last updated on 19/Jul/20

Answered by Dwaipayan Shikari last updated on 19/Jul/20

∫6(√(t^2 +t+(1/4)))dt  6∫(√((t^2 +(1/2))^2 ))dt  6∫(t^2 +(1/2))dt=2t^3 +3t+Constant

$$\int\mathrm{6}\sqrt{{t}^{\mathrm{2}} +{t}+\frac{\mathrm{1}}{\mathrm{4}}}{dt} \\ $$$$\mathrm{6}\int\sqrt{\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dt} \\ $$$$\mathrm{6}\int\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right){dt}=\mathrm{2}{t}^{\mathrm{3}} +\mathrm{3}{t}+{Constant} \\ $$

Answered by bobhans last updated on 19/Jul/20

36t^4 +36t^2 +9 = (6t^2 +3)^2 > 0 ,∀t∈R  ∫ (√((6t^2 +3)^2 )) dt = 2t^3  + 3t + C

$$\mathrm{36}{t}^{\mathrm{4}} +\mathrm{36}{t}^{\mathrm{2}} +\mathrm{9}\:=\:\left(\mathrm{6}{t}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} >\:\mathrm{0}\:,\forall{t}\in\mathbb{R} \\ $$$$\int\:\sqrt{\left(\mathrm{6}{t}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }\:{dt}\:=\:\mathrm{2}{t}^{\mathrm{3}} \:+\:\mathrm{3}{t}\:+\:{C} \\ $$

Commented by DGmichael last updated on 19/Jul/20

����

Terms of Service

Privacy Policy

Contact: info@tinkutara.com