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Question Number 38405 by malwaan last updated on 25/Jun/18

$$\mathrm{If}\mathrm{f}\left(3\right)=3;\mathrm{f}\left(1\right)=2$$$$\Rightarrow {\int }_1^3\mathrm{f}\left(\mathrm{x}\right){\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)\mathrm{dx}=.....$$

Commented by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18

$$plsclarify\left[\left(x\right)\right]isitfloor/greatestinteger$$$$function$$

Commented by malwaan last updated on 25/Jun/18

$$\mathrm{I}\mathrm{am}\mathrm{sorry}$$$$\mathrm{It}\mathrm{is}\mathrm{f}\left(\mathrm{x}\right)$$

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18

$${\int }_1^{3}f\left(x\right)\times \frac{df\left(x\right)}{dx}dx$$$${\int }_1^{3}f\left(x\right)df\left(x\right)$$$$\mid \frac{{\left\{f\left(x\right)\right\}}^2}{2}{\mid }_1^3$$$$=\frac{1}{2}\{f\left(3\right)\times f\left(3\right)-f\left(1\right)\times f\left(1\right)\}$$$$\frac{1}{2}(3^2-2^2)=\frac{5}{2}$$

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