# IntMethod

Method for integral approximation

## Value Summary

 Optional `Exact`, `RiemannLeft`, `RiemannRight`, `RiemannLower`, `RiemannUpper`, `RiemannMiddle`, `RiemannLowerAbs`, `RiemannUpperAbs`, `Simpson`, or `Trapezoid`

## Graphics Primitives

ObjectsIntMethod Default Values
`plot::Integral``Exact`

## Description

`IntMethod` determines the method of the visualization of `plot::Integral` objects.

Following methods are implemented:

• Exact

the area between x-axis and function graph is colored

• RiemannLower

display boxes between x-axis and function graph using the smallest value of the function in each subinterval

• RiemannLowerAbs

display boxes between x-axis and function graph using the smallest absolut value of the function in each subinterval

• RiemannUpper

display boxes between x-axis and function graph using the greatest value of the function in each subinterval

• RiemannUpperAbs

display boxes between x-axis and function graph using the greatest absolut value of the function in each subinterval

• RiemannLeft

display boxes between x-axis and function graph using the function value of the left border in each subinterval

• RiemannMiddle

display boxes between x-axis and function graph using the function value of the middle in each subinterval

• RiemannRight

display boxes between x-axis and function graph using the function value of the right border in each subinterval

• Trapezoid

display an approximation of the integral using the Trapezoidal rule

• Simpson

interpolate the graph of the function using Simpsons rule

## Examples

### Example 1

The following example shows all implemented methods:

```f := plot::Function2d(x*(x-3)*(x+4), Color = RGB::Black): plot(plot::Scene2d(plot::Integral(f, 7, IntMethod = method, Color = [frandom() \$ i=1..3], ShowInfo = [IntMethod, Integral, Error, Position = [-5,90]]), f) \$ method in [RiemannLower, RiemannLowerAbs, Trapezoid, RiemannUpper, RiemannUpperAbs, Simpson, RiemannLeft, RiemannRight, RiemannMiddle], Columns = 3, TextFont = [8], Width = 200, Height = 180)```