Aim of the applet

To approximate the definite integral of a function at a point by Midpoint, Trapezoid and Simpson rules, graphically displaying the respective buildings.

Input data

The function to represent, the ends of integration interval (a and b) and the number of subintervals to be taken (n).

To select which method of integration is to be shown are three boxes in the graph.

Animation button of the value n is located in the lower left corner of the graph.

Output data

Graphical representation of the function.

The areas corresponding to the methods of integrating Midpoint, Trapezoidal or Simpson.

Numeric value of integration for each method.

Value of h (length of subinterval).

Animation of the value n.

First steps

• Approximates the integral of f (x) = sin x on [0, π]. Slide n for the three methods, what is stabilized before?
• If you consider y = x ^ 2 -3, what value n requires Simpson to calculate exact result? Is it the same with y = x ^ 3?