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11.2 Differentials

In the notation here, the integrand denotes the function obtained by differentiating the antiderivative; the differential indicates the variable you differentiate the antiderivative with respect to, to get the integrand.

In the equation

we can interpret dx as an infinitesimal change in the variable x and dA(x) as the corresponding change in A(x). 

With this interpretation we can write

dA = f(x)dx (*)

and applying the integral sign to each sides,

Thus our notation corresponds to the claim that for any antiderivative A we have,