Normally, integration means summing the infinitesimal rectangles of height f(t) and width dt. The differential dt appears as a multiplier behind the integration mark, [itex]\int[/itex], therefore. But, what do you think about summing non-standard infinitesimal pieces, like [itex]\int{1 \over 1/dt + 1}[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

For every dt, it gives some very small value and the sum converges. I know that I can solve this one by the rearrangement [itex]\int{1 \over 1/dt + 1} = \int{dt \over 1 + dt} = \int{dt}[/itex], as dt -> 0. I was puzzled when I had first time to compute this thing. How do you call call it? Is it a usual method to solve this kind of thing?

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# Inrectangular subintegral expression

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