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Calculus is the branch of mathematics which deals with the study of rate of change of quantities. This is usually divided into differential calculus and integral calculus which are concerned with derivatives and integrals respectively. DO NOT USE THIS TAG just because your question makes use of calculus.

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What is distance multiplied by time?

As far as I know, distance $s$ multiplied by time $t$ or (as the differential analogue) the integral $$^{(*)}: \int_{t_0}^{t}s(\tilde{t})\text{d}\tilde{t}\ $$ are not used in the context of physics …
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