Information about integral approximation

Optional | List of arithmetical expressions |

Objects | ShowInfo Default Values |
---|---|

`plot::Integral` | [`2` , `IntMethod` , `Integral` ] |

`ShowInfo`

defines the text information displayed
by `plot::Integral`

.

In `plot::Integral`

, text information about
the used approximation method,
the values of the approximation and the exact integral, the number of subintervals and the error
of the approximation can be displayed within the approximation object.

The attribute is specified by `ShowInfo = [entry`

with a list of
various entries. The user may specify the entries in arbitrary order._{1},
entry_{2}, …]

If the list is empty, no text information is displayed.

Each entry in the list can be of one of the following types:

an arbitrary string

In the text, this entry is appended to the current line. No white space or line break is prepended or appended. The string itself, however, may contain white space or a line break (given by

`\n`

)."" (empty string)

This inserts an empty line in the text.

`IntMethod`

In the text, this creates a new line

`name: float_value`

,where

`name`

is the value of the attribute`IntMethod`

and`float_value`

is the numerical value of the integral approximation. This value is computed internally and inserted in the text, automatically.`IntMethod`

= nameIn the text, this creates a new line

`name: float_value`

,where

`float_value`

is the numerical value of the integral approximation.If

`name`

is one of the flags`RiemannLower`

etc. listed on the help page of the attribute`IntMethod`

, this flag is displayed in the text.Alternatively,

`name`

may be a string. When`name`

is the empty string`""`

, only the numerical approximation of the integral value is displayed.`Integral`

In the text, this creates a new line

`Integral: float_value`

,where

`float_value`

is a high precision float approximation of the exact integral value.`Integral`

= stringIn the text, this creates a new line

`string: float_value`

,where

`string`

is an arbitrary text string and`float_value`

is a high precision float approximation of the exact integral value .When

`string`

is the empty string`""`

, only the high precision approximation`float_value`

is displayed.`Error`

In the text, this creates a new line

`Error: float_value`

,where

`float_value`

is the absolute difference between the numerical value obtained by the chosen approximation method and a high precision float approximation of the exact integral value.`Error`

= stringIn the text, this creates a new line

`string: float_value`

,where

`string`

is an arbitrary text string and`float_value`

is the absolute difference between the numerical value obtained by the chosen approximation method and a high precision float approximation of the exact integral value.When

`string`

is the empty string`""`

, only the absolute quadrature error`float_value`

is displayed.`Nodes`

In the text, this creates a new line

`Nodes: n`

,where the integer

`n`

is the number of intervals used for the integral approximation.`Nodes`

= stringIn the text, this creates a new line

`string: n`

,where

`string`

is an arbitrary text string and the integer`n`

is the number of intervals used for the integral approximation.When

`string`

is the empty string`""`

, only the integer`n`

is displayed.`Position = [X, Y]`

This entry determines the position of the text information.

`X`

and`Y`

are the coordinates of the anchor point of the text. The alignment of the text with respect to the anchor point can be chosen by the attributes`HorizontalAlignment`

and`VerticalAlignment`

.a positive integer

`digits`

The integer

`digits`

determines the number of digits after the decimal point for all following float values.Different float values can be displayed with a different number of digits by inserting several

`digits`

entries at appropriate positions in the list.

Without an explicit specification of ```
Position = [X,
Y]
```

, the text is positioned automatically.

By default, the approximation method, the value of approximation
and the integral is displayed with `2`

digits after
the decimal point:

f := plot::Function2d(x^2, x = -5..5, Color = RGB::DarkGrey): plot(plot::Integral(f, IntMethod = RiemannLower), f)

This call is equivalent to:

plot(plot::Integral(f, IntMethod = RiemannLower, ShowInfo = [2, IntMethod, Integral]), f):

The text can be changed:

plot(plot::Integral(f, IntMethod = RiemannLower, ShowInfo = [IntMethod = "value of the lower Riemann sum", Integral = "exact numerical value", Error = "difference"]), f)

delete f:

The position can be specified explicitely. In this case, the
entries to be displayed must be specified explicitely, too. The text
attribute `VerticalAlignment`

aligns the text object:

f := plot::Function2d(x^2, x = -5..5, Color = RGB::DarkGrey): plot(plot::Integral(f, IntMethod = RiemannUpper, Color = RGB::Lime, ShowInfo = [IntMethod, Integral, Position = [-5, -1]], VerticalAlignment = Top), plot::Integral(f, IntMethod = RiemannLower, Color = RGB::Gold, ShowInfo = [IntMethod, Position = [0, -1]], VerticalAlignment = Top), f)

delete f:

The number of digits after the decimal point can be specified for each value. In the following example all values are displayed with four digits:

f := plot::Function2d(x^2*(x-4)*(x+2), x = -3..5, Color = RGB::Black): plot(plot::Integral(f, 4, IntMethod = Simpson, LineColor = RGB::Red, ShowInfo = [4, IntMethod, Integral, Error]), f)

Only the error shall be displayed with four digits after the decimal point. All other values are shown with only one digit:

plot(plot::Integral(f, 4, IntMethod = Simpson, LineColor = RGB::Red, ShowInfo = [1, IntMethod, Integral, 4, Error]), f)

delete f:

Two approximation objects shall be displayed in one plot. To prevent collision of the automatically positioned texts, we insert an empty line into the text of one of the objects to prevent collision of the automatically positioned texts:

f := plot::Function2d(x^2, x = -5..5, Color = RGB::DarkGrey): plot(plot::Integral(f, IntMethod = RiemannUpper, Color = RGB::Rose, ShowInfo = [IntMethod, "", Integral]), plot::Integral(f, IntMethod = RiemannLower, ShowInfo = [IntMethod, Integral]), f)

Alternatively, the position can be given explicitly:

f := plot::Function2d(x^2, x = -5..5, Color = RGB::DarkGrey): plot(plot::Integral(f, IntMethod = RiemannUpper, Color = RGB::Lime, ShowInfo = [IntMethod, Integral, Position = [-5, -1]], VerticalAlignment = Top), plot::Integral(f, IntMethod = RiemannLower, Color = RGB::Gold, ShowInfo = [IntMethod, Position = [0, -1]], VerticalAlignment = Top), f)

delete f:

The text may contain additional messages:

f := plot::Function2d(x^2, x = -5..5): plot(plot::Integral(f, IntMethod = RiemannUpper, ShowInfo = ["Approximation value:", IntMethod = "", "\nUsed rectangles:", Nodes = ""], Color = RGB::Rose), f)

delete f:

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