Regular partition

Definition

A regular partition is a way of dividing an interval $[a, b]$ into subintervals of equal length. It is used to approximate areas under curves and in the computation of Riemann sums.

5 Must Know Facts For Your Next Test

1. A regular partition of $[a, b]$ into $n$ subintervals means each subinterval has a width $\Delta x = \frac{b - a}{n}$.
2. Regular partitions are essential for the calculation of definite integrals using Riemann sums.
3. The points dividing the interval in a regular partition are called partition points or nodes.
4. In the context of integration, regular partitions help simplify the approximation process by ensuring uniformity in subinterval lengths.
5. Regular partitions can be visualized as equally spaced vertical lines that divide the area under a curve.

Review Questions

• What is the formula for the width of each subinterval in a regular partition?
• Why are regular partitions important in approximating areas under curves?
• How does a regular partition differ from an irregular or arbitrary partition?

Related terms

Riemann Sum:

A method for approximating the total area underneath a curve on a graph, typically by summing up areas of multiple rectangles.

Definite Integral:

The evaluation of the integral of a function over a specific interval $[a,b]$, representing the net area under the curve between those points.

Subinterval:

A smaller division within an interval $[a,b]$, often used in methods like Riemann sums to calculate integrals.