Riemann Sum Calculator — Fórmula
## Riemann Sums
### Concept
A Riemann sum approximates the area under a curve by dividing the interval into rectangles:
1. Divide [a, b] into n equal subintervals, each of width Δx = (b-a)/n
2. For each subinterval, evaluate the function at the left endpoint
3. Sum the areas: S = sum of f(xᵢ) × Δx
### As n → infinity
The Riemann sum converges to the exact definite integral. More rectangles = better approximation.
### Concept
A Riemann sum approximates the area under a curve by dividing the interval into rectangles:
1. Divide [a, b] into n equal subintervals, each of width Δx = (b-a)/n
2. For each subinterval, evaluate the function at the left endpoint
3. Sum the areas: S = sum of f(xᵢ) × Δx
### As n → infinity
The Riemann sum converges to the exact definite integral. More rectangles = better approximation.
Ejemplo Resuelto
Approximate the integral of x² from 0 to 1 with 10 rectangles.
- Δx = (1-0)/10 = 0.1
- Left endpoints: 0, 0.1, 0.2, ..., 0.9
- Sum = (0² + 0.1² + 0.2² + ... + 0.9²) × 0.1
- Exact value = 1³/3 = 0.333333...