Area Under Curve Calculator

Approximate the area under f(x) = x² using trapezoidal, Simpson's, or midpoint rule. Compare with the exact answer.

Lower Bound (a)

Upper Bound (b)

Number of Intervals

Method

Tab to move between fields

Approximate Area

0.33335

Exact Area0.33333

Error Estimate0.000017

How to Use This Calculator

Enter the lower bound (a) and upper bound (b) of integration — the calculator approximates the area under the fixed function f(x) = x² across this interval.
Set the number of intervals to control how finely the range is subdivided; more intervals generally improve accuracy.
Choose a numerical method: Trapezoidal rule (linear segments), Simpson's rule (parabolic segments), or Midpoint rule.
Increase the number of intervals for greater accuracy — Simpson's rule converges fastest for the same interval count.
The shaded area chart visualizes f(x) = x² across [a, b].
Compare the Approximate Area against the Exact Area and Error Estimate to see how closely the chosen method matches the true integral.

How the result changes with Upper Bound (b)

Identify Input Parameters
4 parameters
Lower Bound (a) = 0, Upper Bound (b) = 1, Number of Intervals = 100, Method = 1 = 4 input(s) provided
Calculate Approximate Area
Approximate Area
0.33335 = 0.33335
Calculate Error Estimate
Error Estimate
0.000017 = 0.000017

Engine last updated August 6, 2026. Checked against 4 independently-derived tests — how we verify calculators.

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