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Grade 12 Math Lab: Analysis & Inference FREE

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Riemann Sums & Integration

60 min Grade 12 Math Lab: Analysis & Inference

Learning Objectives

  • Approximate area under curves
  • Understand definite integrals
  • Apply FTC

Key Concepts

Riemann Sum

Sum of rectangle areas approximating integral

Definite Integral

Limit of Riemann sums as n → ∞

Theory

**Riemann Sums:** ∑f(xᵢ)Δx **Types:** - Left: Use left endpoints - Right: Use right endpoints - Midpoint: Use midpoints - Trapezoidal: Average of left and right **Fundamental Theorem:** ∫[a,b] f(x)dx = F(b) - F(a)

Examples

∫[0,2] x² dx

Solution: [x³/3]₀² = 8/3 - 0 = 8/3