# Inrectangular subintegral expression

1. Jul 28, 2011

### valjok

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, $\int$, therefore. But, what do you think about summing non-standard infinitesimal pieces, like $\int{1 \over 1/dt + 1}$?

For every dt, it gives some very small value and the sum converges. I know that I can solve this one by the rearrangement $\int{1 \over 1/dt + 1} = \int{dt \over 1 + dt} = \int{dt}$, 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?