What Is the Trapezoid Rule?
Sometimes, finding the exact value of a definite integral is difficult — either because the function has no neat antiderivative, or because you only have a table of data points rather than a formula. In these situations, numerical methods let us estimate the area under a curve without doing exact integration.
The trapezoid rule is one of the most important numerical integration methods at SL level.
A numerical method that approximates the definite integral (i.e. the area under a curve) by dividing the region into a series of trapezoids and summing their areas.
The core idea is simple:
- Divide the interval into equal strips.
- Over each strip, approximate the curve with a straight line connecting the two endpoints — this creates a trapezoid.
- Add up the areas of all the trapezoids.
The trapezoid rule is particularly valuable when working with discrete data (e.g. values recorded in a table) or with functions that are too complex to integrate analytically.