What does the integral sign represent in calculus?

The integral sign in calculus represents the concept of accumulation, specifically the cumulative sum of infinitesimals. When we perform an integral, we are essentially summing up infinitely small quantities over a specific interval. This process allows us to calculate the area under a curve, among other things.

In the context of indefinite integrals, the integral symbol indicates the collection of these infinitesimal contributions, resulting in a function. In definite integrals, it illustrates the accumulation of these infinitesimal elements over a specified range, leading to a finite value that represents total accumulated quantity.

The choice reflecting the cumulative sum of infinitesimals aligns perfectly with the fundamental idea behind integration, highlighting its role in measuring continuous quantities, rather than merely being a finite sum or product of separate terms.