When we think of a Riemann integral, it is usually defined as $\lim_{\Delta x_{k}\rightarrow 0}\sum_{k = 1}^{n}f(x_{k}^{*})\Delta x_{k} = \int_{a}^{b}f(x)~dx$. This means that $f(x)$ should be interpreted as the value of $f$ at $x$, since we are multiplying function values by "infinitesimal intervals." Therefore, how is integration an operation on functions, when the integrand is not a function but the output of a function at $x$?
2026-05-15 06:46:10.1778827570
Interpretation of an integral of a function $f$
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