Numerical Integration

Trapezoids and Simpson

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The trapezoidal rule approximates a curve with straight segments.
• Its error shrinks by about 4× each time the number of strips doubles.
• Simpson’s rule uses parabolas and is far more accurate for smooth functions.

Steps

1. Trapezoids
2. How many strips?
3. Simpson’s rule
4. Trapezoids versus Simpson
5. Two trapezoids
6. Simpson on a sine