Calculus & Numerical Methods

Simpson's Rule Integration

Definite integral via Simpson's rule.

Formula

Formula
ab f dx ≈ (h3)(f0 + 4f1 + 2f2 + … + fn)

Variables

SymbolDefinitionType & rangeUnitsRole
f integrand expression / text x input
a, b limits real number (ℝ) input
n even intervals integer (ℤ) input

Try it yourself

Interactive calculator
math expression (e.g. x*x, sin(x))
Result

Worked examples

Example 1
Givenf(x) = sin(x), a = 0, b = 3.141592654, intervals n = 1000
Result2
Example 2
Givenf(x) = x*x, a = 0, b = 3, intervals n = 1000
Result9