What-do-we-mean-by-f-x-dx-

Question Number 66293 by Rio Michael last updated on 12/Aug/19

$${What}\:{do}\:{we}\:{mean}\:{by}\:\: \\ $$$$\:\:\int_{−\infty} ^{+\infty} {f}\left({x}\right)\:{dx}? \\ $$

Commented by mathmax by abdo last updated on 12/Aug/19

$$\int_{−\infty} ^{+\infty} {f}\left({x}\right){dx}\:={lim}_{\xi\rightarrow+\infty} \:\:\int_{−\xi} ^{\xi} {f}\left({x}\right){dx}\:\:{and}\:\int_{−\xi} ^{\xi} {f}\left({x}\right){dx}\:{is}\:{the}\:{surface} \\ $$$${limiteted}\:{by}\:{y}=\mathrm{0}\left(\:\:\left({x}^{'} {ox}\right)\right)\:{and}\:{y}={f}\left({x}\right) \\ $$

Commented by mathmax by abdo last updated on 12/Aug/19

$$\left.{on}\right]−\xi,\xi\left[…\right. \\ $$

Commented by Rio Michael last updated on 13/Aug/19

$${thanks} \\ $$

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