notesonly.in

One notebook for every subject — open it anywhere.

Log in

Trapezoidal rule

General · Mathematics

Study notes

Q: Approximate ∫₀¹ x² dx by trapezoidal with n = 2. Compare exact. h = 0.5. Points: 0, 0.5, 1. T = (h/2)[f₀+2f₁+f₂] = 0.25[0+2(0.25)+1] = 0.25(1.5) = 0.375. Exact: 1/3 ≈ 0.3333. Error: 0.0417! O(h²) = O(0.25) ✓. (Trapezoids overestimate convex!)

← Back to topics for Mathematics