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Trapezium Rule (Strip) Calculator

Approximating area under a curve.

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Strip Area

Formula first

Overview

The Trapezium Rule provides a linear approximation for the area under a curve by treating a single interval as a trapezoid. It essentially calculates the product of the interval width and the arithmetic mean of the two boundary heights.

Symbols

Variables

A = Strip Area, h = Width, y_0 = Left Height, y_1 = Right Height

Strip Area
Width
Left Height
Right Height

Apply it well

When To Use

When to use: Use this method when you need to estimate a definite integral for data sets where only discrete points are known. It is most effective when the interval width is small or the function behaves relatively linearly across the chosen segment.

Why it matters: This rule is fundamental in numerical analysis and engineering for calculating total values from rate data, such as finding distance from velocity or energy from power. It provides a simple yet effective way to process sensor data in real-time computing environments.

Avoid these traps

Common Mistakes

  • Wrong h measurement.
  • Counting endpoints twice.

One free problem

Practice Problem

A surveyor measures the depth of a river at two points 4 meters apart. The depth at the first point is 1.5 meters and at the second point is 2.2 meters. Estimate the cross-sectional area of this strip of the river.

Width4
Left Height1.5
Right Height2.2

Solve for:

Hint: Multiply half the width by the sum of the two depths.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Calculus: Early Transcendentals by James Stewart
  2. Numerical Analysis by Richard L. Burden and J. Douglas Faires
  3. Wikipedia: Trapezoidal rule
  4. Chapra, Steven C., and Raymond P. Canale. Numerical Methods for Engineers. 7th ed. McGraw-Hill Education, 2015.
  5. Edexcel A-Level Mathematics — Pure (Numerical Methods)