Definite Integral Calculator

Use our free definite integral calculator to compute ∫ₐᵇ f(x) dx using Simpson's rule, trapezoidal rule, or compare both methods side by side.

Math

Method

f(x) =

Lower bound

Upper bound

Partitions

Formula

Numerical definite integration using Simpson's 1/3 rule (4th order accuracy) or the trapezoidal rule (2nd order). Compare both to estimate error.

Simpson: (h/3)(f₀+4f₁+2f₂+...+fₙ), Trapezoidal: h(½f₀+f₁+...+½fₙ)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select Simpson, Trapezoidal, or Compare.
2Enter f(x) and bounds.
3Adjust partitions if desired.
4Click Calculate.

Examples

∫₀¹ x² (Simpson)

1.Exact: 1/3 = 0.33333

Result: 0.3333333333

Compare for sin(x)

1.Simpson more accurate than trapezoidal for smooth functions

Result: 2

Frequently Asked Questions

Simpson is O(h⁴) accurate; Trapezoidal is O(h²). Simpson is preferred for smooth functions.

Yes, any expression with x is supported.

Simpson's rule is significantly more accurate for smooth functions.

Shows both results and their difference.

Higher n = more accurate but slower.

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CalculateMe Team

Last updated: 2026-07-14

Definite Integral Calculator

Formula

How It Works

Examples

∫₀¹ x² (Simpson)

Compare for sin(x)

Frequently Asked Questions

Simpson vs Trapezoidal?

Can I use any function?

Which is more accurate?

What is the comparison mode?

What does n affect?

Related Calculators

Definite Integral Calculator

Formula

How It Works

Examples

∫₀¹ x² (Simpson)

Compare for sin(x)

Frequently Asked Questions

Simpson vs Trapezoidal?

Can I use any function?

Which is more accurate?

What is the comparison mode?

What does n affect?

Related Calculators