Use this numerical method to approximate a derivative or definite integral from a callable expression and explicit step or interval settings.

Samples

Function samples at evenly spaced points, first at xMin and last at xMax.

xMin

Lower integration bound.

xMax

Upper integration bound.

Approximate a definite integral from evenly spaced samples over [xMin, xMax] using the composite trapezoidal rule. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Integral

Trapezoidal approximation of the integral.

Delta x

Sample spacing implied by the bounds.

• Numerical differentiation and integration introduce truncation and floating-point error. Discontinuities, singularities, oscillation, cancellation, or an unsuitable step size can make a plausible-looking result inaccurate.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Repeat the calculation with a finer resolution and compare the change. Use symbolic calculus or an adaptive high-precision method when an exact result or controlled error bound is required.

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