Trapezoidal Rule Calculator

Approximate definite integrals using the trapezoidal rule. Calculate area under curves with customizable subintervals.

Use: + - * / ^, sqrt(), sin(), cos(), tan(), ln(), exp()
Higher n = more accurate approximation

Approximation Result

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Error Estimation

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Summary

Step Size (h):-
Subintervals:-
Function Points:-

Step-by-Step Solution

Enter a function and bounds, then click "Calculate Approximation" to see the step-by-step solution.

Trapezoidal Rule Formula

∫ab f(x) dx ≈ (h/2)[f(x₀) + 2f(x₁) + 2f(x₂) + ... + 2f(xn-1) + f(xn)]

Where h = (b - a)/n and xi = a + i·h

Error Formula

|E| ≤ (b-a)³ / (12n²) × max|f''(x)|

Error decreases as 1/n² (quadratic convergence)

When to Use

  • No antiderivative exists
  • Function is only known at points
  • Need quick approximation
  • Data from experiments