## `student::plotTrapezoid` -- plot of a numerical approximation to an integral using the Trapezoidal rule

#### Introduction

`student::plotTrapezoid``(f, x=a..b, n)` computes a numerical approximation to the integral int(f(x),x=a..b) using the Trapezoidal rule and returns a plot of the numerical process.

#### Call(s)

`student::plotTrapezoid(f, x=a..b <, n> <, opt1>...)`

#### Parameters

`f` | - | functional expression in `x`
`x` | - | identifier
`a, b` | - | arithmetical expressions
`n` | - | a positive integer (number of trapezoids to use)
`opt1` | - | plot option(s) for two-dimensional graphical objects

#### Returns

a graphical object of the domain type `plot::Group`.

#### Related Functions

`plot`, `plot::Group`, `student::plotRiemann`, `student::plotTrapezoid`, `student::trapezoid`

#### Details

- `student::plotTrapezoid``(f, x=a..b, n)` computes a numerical approximation to the integral int(f(x),x=a..b) using the Trapezoidal rule and returns a graphical object of the numerical process that can be displayed with the function `plot`.
- `n` is the number of trapezoids to use. The default value is 4.
- The plot options `opt1`... must be valid plot options for two-dimensional graphical objects. See `plot2d` for details.

  Note that scene options are not allowed! You may give scene options as optional arguments for the function `plot`, or use `plot::Scene` to create an object representing a graphical scene.

- The graphical object returned has three operands: a group of the (filled) trapezoids, a group of polygons representing the frames of the trapezoids, as well as the function graph of `f` (of the domain type `plot::Function2d`). The first two operands are objects of the domain `plot::Group`.

#### Example 1

The following call returns a visualization of the numerical approximation to the integral int(cos(x),x=0..PI/2) = 1 using the Trapezoidal rule and 10 trapezoids:

    >> p := student::plotTrapezoid(cos(x), x = 0..PI/2, 10)

                                   plot::Group()

To display it on the screen, call:

    >> plot(p)

#### Example 2

You can change plot parameters of the visualization returned by `student::plotTrapezoid`. For example, to change the x-range of the graph of f, we set the attribute `range` of the last operand of `p` to the value `x = -PI/2..PI/2`:

    >> (p[nops(p)])::range := x = -PI/2..PI/2:
       plot(p)

#### Changes

- new function

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