﻿ Trapezoidal Rule Calculator - MathDeft

# Trapezoidal Rule Calculator

## What is a trapezoidal rule calculator?

The trapezoidal rule is one of the families of formulas used for numerical integration usually introduced during first-year calculus. In the field of mathematics involving statistical analysis, the trapezoidal rule is a technique that is utilized to approximate values of definite integrals. The key to implementing trapezoidal rule calculator is assuming the area of the integral, ie. the area under the graph to be a trapezoid.

## How to use the trapezoidal rule calculator?

Assuming the area under the graph to be a trapezoid, the approximate value of the integral can be calculated using the following formula:

For a more accurate approximation, partitioning of the integral sum can be done, and then the trapezoidal rule can be applied to each subinterval and finally summed to obtain the result.

## What is a trapezoidal Rule?

This rule is an approximate method to find the value of definite integrals, thus introducing some minor errors in our results. For finding errors in the approximation, we need to find an upper bound on the second derivative throughout integration, which is a hectic task. However, with time, graphing devices such as a graphing calculator has been developed which can be used easily by anyone to find the upper bound and hence estimate the approximate error of the integral.
Trapezoidal rule error is of high importance. It can be calculated using the given formula: