Riemann integral

The Riemann integral is a special way to find the area under a curve on a graph. It was created by a clever mathematician named Bernhard Riemann. He shared his idea at the University of Göttingen in 1854.

This way of measuring area helps us solve many useful problems. Imagine you want to find out how much space is under a wiggly line. The Riemann integral lets us break that space into tiny pieces, like small rectangles, and then add up all those pieces. By making the pieces very thin, we can get a really good guess of the real area.

The Riemann integral is very important in mathematics, especially in a part called real analysis. It helps scientists and engineers measure things and understand how different parts fit together. For many common curves, we can find the exact area using a rule called the fundamental theorem of calculus.

!The integral as the area of a region under a curve.

The ideas from the Riemann integral also help us learn about other kinds of integrals, like the Lebesgue integral and the Riemann–Stieltjes integral. These are useful for more advanced math, but they all started with Riemann’s smart thinking.