Posts Tagged ‘trapezoid’

Composite Figures

Friday, November 13th, 2009

An Overview of Composite Figures

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Description

A detailed tutorial on what composite figures are. Step by step tutorial including several examples of how to identify composite figures for reference.

Overview

A composite figure is any figure that can be split into more than one shape. Hardly any regular shapes are considered to be composite shapes. The only one is a regular trapezoid – it can be split into three shapes, two triangles and a rectangle. You could technically consider a rectangle to be a composite figure – you can split it into squares or smaller rectangles – but since it doesn’t need to be split into different shapes to solve for area, then it is not considered a composite figure.

Error Bounds: Trapezoidal Rule

Friday, September 25th, 2009

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)).