Key Concepts

• • A Riemann sum approximates ∫ f(x)dx as a sum of rectangle areas
• • Left rule: uses f at the left edge — overestimates for increasing functions
• • Right rule: uses f at the right edge — underestimates for increasing functions
• • Midpoint rule: uses f at the midpoint — generally more accurate than left/right
• • Error → 0 as n → ∞; the definite integral is the limit of the Riemann sum