Definite Integral Calculator

This definite integral calculator finds the value of an integral between a lower and an upper limit, which is the signed area between the curve and the horizontal axis over that interval. The definite integral is one of the most important tools in calculus and applied maths, used to work out total distance from a speed graph, the work done by a varying force, the area of an irregular region, average values, probabilities under a distribution, and much more. Area that sits above the axis counts as positive and area below counts as negative, so the result is a net signed area. You enter the function of x, then the lower and upper limits, which may be numbers or expressions using pi and e, and the calculator returns the value. It works by numerical integration using Simpson's rule, which slices the interval into many thin strips, fits a parabola across each one, and sums the pieces, giving an answer accurate to many decimal places for smooth functions. This numeric approach has a real advantage: it works even for functions that have no neat antiderivative in elementary form, where a symbolic method would fail. For an antiderivative as an expression, use the companion integral calculator. Enter a function and two limits to see the value straight away.

Use * for multiply and ^ for powers; pi and e are allowed. Computed by Simpson's rule with 1000 strips. Functions with breaks inside the interval may be less accurate. Estimate only.