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

Select a function type (polynomial, trig, exponential, or logarithmic) and enter its parameters.
Set the lower bound (a) and upper bound (b) of integration on the x-axis.
Choose a numerical method: Trapezoidal rule (linear segments), Simpson's rule (parabolic segments), or Midpoint rule.
Increase the number of sub-intervals (n) for greater accuracy — Simpson's rule achieves high precision with fewer intervals.
The shaded area chart visualizes the region between the curve and the x-axis across [a, b].
A negative area indicates the curve lies below the x-axis; the calculator returns the signed integral value.

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