Graph of the area below a curve : plotarea areaplot

• With two arguments, plotarea shades the area below a curve.
  plotarea(f(x),x=a..b) draws the area below the curve y = f (x) for a < x < b, i.e. the portion of the plane defined by the inequations a < x < b and 0 < y < f (x) or 0 > y > f (x) according to the sign of f (x) .
  Input :
  plotarea(sin(x),x=0..2*pi)
  Output :
  the portion of plane locates in the two archs of sin(x)
• With four arguments, plotarea represents a numeric approximation of the area below a curve, according to a quadrature method from the following list:
  trapezoid,rectangle_left,rectangle_right,middle_point.
  For example plotarea(f(x),x=a..b,n,trapezoid) draws the area of n trapezes : the third argument is an integer n, and the fourth argument is the name of the numeric method of integration when [a, b] is cut into n equal parts.
  Input :
  plotarea((x^2,x=0..1,5,trapezoid)
  If you want to display the graph of the curve in contrast (e.g. in bold red), input :
  plotarea(x^2,x=0..1,5,trapezoid); plot(x^2,x=0..1,display=red+line_width_3)
  Output :
  the 5 trapezes used in the trapezoid method to approach the integral
  Input :
  plotarea((x^2,x=0..1,5,middle_point)
  Or with the graph of the curve in bold red, input :
  plotarea(x^2,x=0..1,5,middle_point); plot(x^2,x=0..1,display=red+line_width_3)
  Output :
  the 5 rectangles used in the middle_point method to approach the integral