Summer of Math Exposition

well written without too much riggor. I liked it. Could have used simulations to explain better.

This is a well written article on integration. The author tries to move away from the conventional definition and help students gain a deeper understanding.

The article would benefit greatly from more diagrams or animations or interactive parts to make it clear to the reader how this understanding of integration is different or superior.

There are many possible visual examples from physics or geometry that would also help the reader further. Even the rotational solids mentioned are not shown in the diagram.

The article is well written and easy to understand for its aimed audience. It is formatted nicely and contains helpful examples but I think fundamentally it doesn’t really go ‘beyond area under a curve’. The ways to understand integrals given in this article are still basically sums of areas which, while technically aren’t under the curve, are still quite similar to the original interpretation. There are so many unique and wonderful ways to think about integrals in mathematics but this article goes beyond by providing near equivalent alternatives.

It gave problems that clearly motivated the more general way of thinking about integration.

The explanation was good but I don’t feel like it’s saying anything new or not well understood.

Thinking about integration as a sum is very well known.