ADV017 · Advanced mathematics · Class 12 + B.Tech
Numerical approximation
Numerical methods approximate answers that are hard to find exactly. The trapezium rule estimates an integral with straight-topped strips.
≈ ∫Numerical approximation
📐 Formula
∫ₐᵇ f ≈ (h/2)[f₀ + 2(f₁ + … + fₙ₋₁) + fₙ], h = (b − a)/n
✏️ Worked example
∫₀^π sin x dx with 4 strips ≈ 1.896; the exact value is 2. Doubling the strips cuts the error about four times.
🌍 Where it is used
Engineering calculations, computer simulations.
❓ Quick check
More strips in the trapezium rule usually…
🏋️ Practice
EasyTrapezium rule for ∫₀² x dx with 1 strip?
Answer: 2 (exact for straight lines)
MediumError with 4 strips above?
Answer: ≈ 0.104
ChallengeName another numerical integration rule.
Answer: Simpson's rule