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Question Number 115892 by mohammad17 last updated on 29/Sep/20

Answered by Dwaipayan Shikari last updated on 29/Sep/20

$${\int }_0^4\mathrm{xlogxdx}$$$${\left[\frac{{\mathrm{x}}^2}{2}\mathrm{logx}\right]}_0^4-{\left[\frac{{\mathrm{x}}^2}{4}\right]}_0^4$$$$8\log \left(4\right)-4$$

Commented by mohammad17 last updated on 29/Sep/20

$$bysimpsonsir$$

Commented by mathmax by abdo last updated on 29/Sep/20

$$\mathrm{he}\mathrm{gives}\mathrm{the}\mathrm{solution}\mathrm{by}\mathrm{pimpon}....$$

Commented by Dwaipayan Shikari last updated on 30/Sep/20

$${\int }_0^4\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\frac{4-0}{6}(\mathrm{f}\left(0\right)+4\mathrm{f}\left(\frac{4}{2}\right)+\mathrm{f}\left(\mathrm{b}\right))$$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{xlogx}$$$$\mathrm{f}\left(0\right)=\underset{x\to 0}{\lim xlogx}=\mathrm{x}(\mathrm{x}-1)=0$$$${\int }_0^4\mathrm{f}\left(\mathrm{x}\right)=\frac{2}{3}(4.2\log \left(2\right)+4\log 4)=\frac{32}{3}\log \left(2\right)=7.3935.\left(\mathrm{approx}\right)$$$$\mathrm{Actual}\mathrm{result}=16\log \left(2\right)-4=7.090..$$

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