# Simpson's Rule

- Author:
- Dr. Doug Davis, 3D

This applet shows three points on a curve separated in by . Straight dotted lines connect the points.
Moving the blue dot will change the location.
Moving the black dots will change the function.
There are three check boxes.

- Trapezoids shows the areas that would be used for trapezoid numerical integration.
- Parabola shows a quadratic equation fit through the three points.
- Simpson's Rule shows the area that would be used for Simpson's rule integration.

Trapezoids
Note the area between the trapezoids and the curve. This would result in an error in the approximation.
How does this area vary as is decreased?
Parabola
How close is the parabola to the functions curve?
How does this compare to the straight lines?
Is the comparison the same as you move and change ?
Simpson's Rule
How does the area for Simpson's rule integration compare to the actual area under the curve?
Does it appear that Simpson's rule area or trapezoid method would better approximate the true area under the curve?