Integral Calculator

Use our free integral calculator to compute definite integrals numerically using Simpson's rule. Supports any function with configurable partitions.

Math

f(x) =

Lower bound

Upper bound

Partitions (even)

Formula

Compute the definite integral of any function using Simpson's 1/3 rule. For smooth functions, error decreases as O(h⁴) with partition size.

∫ₐᵇ f(x) dx ≈ (h/3) × [f₀ + 4f₁ + 2f₂ + 4f₃ + ... + fₙ]

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter f(x) using x as variable.
2Enter lower and upper bounds.
3Optionally adjust partitions.
4Click Calculate.

Examples

∫₀¹ x² dx

1.∫₀¹ x² = [x³/3]₀¹ = 1/3 ≈ 0.33333

Result: 0.3333333333

∫₀^π sin(x) dx

1.∫₀^π sin(x) = [−cos(x)]₀^π = 2

Result: 2

Frequently Asked Questions

Simpson's 1/3 rule — composite with even partitions.

O(h⁴) — partitions ×4 reduces error ×256 for smooth functions.

sin, cos, tan, exp, ln, sqrt, abs, polynomials — any expression.

Use a large upper bound as an approximation.

It's automatically rounded up to the next even number.

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CalculateMe Team

Last updated: 2026-07-14

Integral Calculator

Formula

How It Works

Examples

∫₀¹ x² dx

∫₀^π sin(x) dx

Frequently Asked Questions

What method is used?

What is the error?

What functions are supported?

Can I integrate to infinity?

What if n is odd?

Related Calculators

Integral Calculator

Formula

How It Works

Examples

∫₀¹ x² dx

∫₀^π sin(x) dx

Frequently Asked Questions

What method is used?

What is the error?

What functions are supported?

Can I integrate to infinity?

What if n is odd?

Related Calculators