What is Integration Simpson Rule Calculator and Why it Matters?
Simpson’s rule provides high-accuracy numerical approximation of definite integrals when an antiderivative is unavailable.
Mathematical Formula and Theory
∫_a^b f(x) dx ≈ (h/3)[f(x₀)+4f(x₁)+2f(x₂)+…+f(xₙ)], exact for cubics, error O(h⁴).
How to Use This Calculator - Step by Step
- Enter integrand, limits, and even number of intervals.
- Click Integrate.
Solved Example with Full Calculation
∫₀^π x² sin(x) dx with n=4 yields ≈ 5.87, matching the exact value π²−4 ≈ 5.87.