# Why do some of my, usually international/Indian students, write limits to the left of the integral?

I see a lot of my students (I am in the US), usually Indian, write the limits of integration to the LEFT of the integral sign rather than customary top or right. The formula will look for example like ${}_5^7 \int \sin(t)dt$.

Is this standard in India?

• I have observed two English students in the UK, doing the same thing. For one of them it is a personal choice, for the other, her high-school teacher's way of writing the limits of integral. – Amir Asghari Mar 4 '17 at 8:36
• Now that I read this, I do recall having seen this. Or even sometimes ${}_5\int^7$. I speculate that the original hand-written method had the limits directly above and below the integral sign, but for typesetting it was preferable to move them to one side or the other. – Gerald Edgar Mar 4 '17 at 16:09
• @GeraldEdgar I would say that still is at least a quite common way to write integrals (i.e. limits above and below). This most probably depends on country and I'm guessing the fact that the usual way to write limits in tex is with sub/superscripts that will become the new norm. Though of course latex does provide $\int\limits_{a}^{b} x\;dx$. – DRF Mar 7 '17 at 10:29

## 1 Answer

First, Cajori's The History of Notations of the Calculus presents a rather unproblematic history of various notions suggested for the definite integral and none has the limits of integration written on the left.

Second, I checked the textbooks published by The [Indian] National Council of Educational Research and Training (NCERT). They publish textbooks in English, Hindi, and Urdu. The English and the Hindi versions of Year 12 textbook where we can find definite integrals write them as we do. I couldn't find the Urdu version.

Third, and this is the most interesting of all, I checked a number of Youtube videos of some of "famous" (according to the number of viewers) Indian mathematics teachers. They mostly write the lower limit inside on the RIGHT of the integral sign and the upper integral outside on the LEFT of the integral sign. Here are two snapshots of two different teachers.