Math · Calculus

Integral Calculator

Evaluate definite integrals numerically with the trapezoidal rule and Simpson's rule — no antiderivative required.

Function f(x)

Lower limit a

Upper limit b

Subintervals n

Method

Definite integral

Trapezoidal approximation

Simpson's approximation

Difference |S − T|

Step size h

f(a), f(b)

Trapezoidal rule: ∫f dx ≈ h/2 · [ f(a) + 2Σf(x_i) + f(b) ]
Simpson's rule: ∫f dx ≈ h/3 · [ f(a) + 4Σ_oddf(x_i) + 2Σ_evenf(x_i) + f(b) ]
Supported syntax: x, ^ (power), sin(x), cos(x), tan(x), exp(x), log(x) (natural), sqrt(x), abs(x), pi, e.

Any integrable function

Type x^2, sin(x)/x, exp(-x^2) and more — the numeric engine handles the rest.

Two classic rules

Trapezoidal and Simpson's rules with adjustable step count for accuracy.

Error insight

Comparing both methods reveals the convergence of the approximation.

Up to 100k steps

Increase n for tight precision on oscillatory or steep functions.

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