Definite Integral Calculator
Approximates a definite integral ∫ f(x) dx over [a, b] using composite Simpson's rule with 1000 intervals — accurate to many decimal places for smooth functions. This is a numeric approximation, not a symbolic antiderivative, so it works for functions that don't have a closed-form integral, like e^(-x²) or sin(x)/x.
Simpson's rule fits a parabola through each pair of adjacent intervals rather than a straight line (as the simpler trapezoidal rule does), which converges to the true value much faster for smooth, continuous functions. With 1000 intervals the error is typically negligible for well-behaved functions across a reasonable bound range.
Typical use cases: checking a hand-calculated integral from a calculus course, evaluating an integral that has no elementary antiderivative, or quickly estimating area-under-curve for a function defined by an equation rather than a data table.
Enter any expression using standard math notation, set your bounds, and the result updates instantly.