what does $dx$ mean in: $$\int f(x)dx$$ and is it true that, if $\frac{df(x)}{dx} = g(x)$, then: $$\int g(x)dx = \int df(x)$$
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take the XY coordinate system. Integration means the calculation of area basically. So when we use $A=l*b$ in mensuration usually here our breadth is the infinitesimal change in the value of $x$ that is $dx$ into the value of length which is on the $y$ axis and it’s the function $f(x)$.
The entire essence is calculation of area of the continuous bodies. Integration means adding up those infinitely small areas that you calculated to form the entire surface.
Fourier_T
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So my second statement is true? – explorer Nov 05 '20 at 21:13
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Differentiation of $f(x)$ is $g(x)$ so multiply both sides by d(x) and integrate. You’ll have : – Fourier_T Nov 06 '20 at 03:12
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$\int g(x)d(x)=f(x)$ – Fourier_T Nov 06 '20 at 03:13
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1$df(x) = g(x) d(x)$, $\int df(x) = \int g(x)d(x)$, $\int df(x) = f(x)$. Thank you. – explorer Nov 06 '20 at 03:41