Trapezoidal approximation method
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Trapezoidal approximation method
A more tedious yet more precise method of approximating the area under a curve, using trapezoids along with the formula for the area of a trapezoid, . For estimating areas under curves, this formula is changed slightly, shown in the picture below.
- Index
Chapter 7 - Trapezoidal Method
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Trapezoidal rule
The trapezoidal rule approximates a definite integral using a straight segment between each pair of adjacent endpoint values. Each piece contributes its width times the average of its two endpoint heights. For example, one trapezoid for x² on [0,2] has width 2 and heights 0 and 4, giving 4. For a concave-up function the trapezoidal sum overestimates the integral, while for a concave-down function it underestimates it.