How does Simpson's rule use three points and a parabola to approximate an integral?

Conditions

• Uses three points of the function on the integration interval.
• Exact for constant, linear, and quadratic functions according to the lecture statement.

Reasoning, step by step

1. Choose three points of the function.
2. Fit those three points to a parabola.
3. Integrate the parabola to get the numerical approximation.
4. Recognize that this method is exact for constants, linear functions, and parabolas.

Example

The video defines Simpson's rule as a numerical integration method that fits three points of the function to a parabola and integrates that parabola. The lecturer explicitly states that this method integrates exactly any functions that are constants, linear, or parabolas.

Common misconceptions

• Thinking Simpson's rule is useful only because the target function is literally a parabola.
• Assuming Simpson's rule is exact for all types of functions.

Watch the explanation

Explore next

• Which functions does Simpson's rule integrate exactly according to this lecture?
• What is Romburg integration in relation to Simpson's rule?