These sorts of approximations are called Riemann sums, and they're a foundational tool for integral calculus. Our goal, for now, is to focus on understanding two types of Riemann sums: left Riemann …

Riemann sums help us approximate definite integrals, but they also help us formally define definite integrals. Learn how this is achieved and how we can move between the representation of area as a …

Approximating the area under a curve using some rectangles. This is called a "Riemann sum".

Riemann sums is the name of a family of methods we can use to approximate the area under a curve. Through Riemann sums we come up with a formal definition for the definite integral.

Review how we use Riemann sums and the trapezoidal rule to approximate an area under a curve.

Summation notation (or sigma notation) allows us to write a long sum in a single expression. While summation notation has many uses throughout math (and specifically calculus), we want to focus on …

Riemann sums are approximations of area, so usually they aren't equal to the exact area. Sometimes they are larger than the exact area (this is called overestimation) and sometimes they are smaller …

Which of the following approximates the area between f (x) and the x -axis on the interval [0, 2] using a left Riemann sum with 6 equal subdivisions?

Given a definite integral expression, we can write the corresponding limit of a Riemann sum with infinite rectangles.

Review how we use Riemann sums and the trapezoidal rule to approximate an area under a curve.