Question Number 90198 by M±th+et£s last updated on 21/Apr/20
$$\int{sin}\left({dx}\right)\: \\ $$
Commented by mr W last updated on 22/Apr/20
$${it}'{s}\:{not}\:{a}\:{defined}\:{thing}! \\ $$
Commented by M±th+et£s last updated on 22/Apr/20
$${i}\:{think}\:{sir}\:{tanmy}\:{solution}\:{is}\:{correct} \\ $$
Commented by mr W last updated on 22/Apr/20
$${as}\:{i}\:{said}\:{things}\:{like}\:\int{f}\left({dx}\right)\:{don}'{t} \\ $$$${exist}\:{because}\:{they}\:{are}\:{not}\:{defined}. \\ $$$${dx}\:{is}\:{not}\:{a}\:{variable}\:{or}\:{a}\:{value}. \\ $$$$\int{f}\left({x}\right){dx}\:{is}\:{defined}\:{as}: \\ $$$$\int{f}\left({x}\right){dx}={F}\left({x}\right)\equiv\frac{{dF}\left({x}\right)}{{dx}}={f}\left({x}\right) \\ $$$${both}\:\int\:{and}\:{dx}\:{are}\:{just}\:{symbols}. \\ $$$$ \\ $$$${can}\:{you}\:{tell}\:{what}\:\int{f}\left({dx}\right)\:{means}? \\ $$
Answered by frc2crc last updated on 22/Apr/20
$${it}\:{x}+{C} \\ $$
Commented by M±th+et£s last updated on 22/Apr/20
$${yes}\: \\ $$
Answered by TANMAY PANACEA. last updated on 22/Apr/20
$${sin}\left({dx}\right)\approx{dx} \\ $$$$\int{dx} \\ $$$$={x}+{c} \\ $$$$ \\ $$$$ \\ $$
Answered by M±th+et£s last updated on 22/Apr/20
$${I}=\int\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{lim}}\:{sin}\left(\bigtriangleup{x}\right) \\ $$$$=\int\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\bigtriangleup{x}\right)}{\bigtriangleup{x}}\:\bigtriangleup{x} \\ $$$$=\int\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{lim}}\frac{{sin}\left(\bigtriangleup{x}\right)}{\bigtriangleup{x}}\:\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{lim}}\left(\bigtriangleup{x}\right) \\ $$$${I}=\int{dx}={x}+{c} \\ $$