Error Bounds: Trapezoidal Rule

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Using the Trapezoidal Rule to Solve Error Bounds

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Description

 

 

A detailed tutorial on using the trapezoidal rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the trapezoidal rule for reference.

 

 

 

Overview

 

 

The trapezoidal rule is a rule in calculus that is used to solve error bounds and evaluate the definite integral  \int_{a}^{b} f(x)\,dx. 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:

 \int_{a}^{b} f(x)\, dx \approx (b-a)\frac{f(a) + f(b)}{2}.

The least complicated form of the trapezoidal rule is expressed as:

 T = \tfrac12 (b-a) (f(a)+f(b)).
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