Using the Midpoint Rule to Solve Error Bounds
Description
A detailed tutorial on using the midpoint rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the midpoint rule for reference.
Overview
The midpoint rule, also known as the rectangle method, is the easiest way of solving error bounds. The region under the graph of a function is sectioned off into rectangles of equal width. You then must find the areas of these rectangles. Then all the areas are added together to find the approximation of the integral. The formula for this is:
The least complicated form of the midpoint rule is expressed as:
The way that the trapezoidal rule works is that you take the region under a graph, approximate it as a trapezoid, and calculate the area. As a mathematical formula, this is the trapezoidal rule:
