The area under a curve f(x) from a to b is approximated by dividing [a,b] into n rectangles. Left Riemann: use f(xᵢ). Right: use f(xᵢ₊₁). Midpoint: use f((xᵢ+xᵢ₊₁)/2). Trapezoidal: average left and right. As n→∞, all methods converge to the true integral ∫f(x)dx.
How to Use
Select a function and bounds:
- Function: Choose from presets
- Bounds: Set a and b
- Rectangles: Adjust n
Methods
- Left: underestimates if increasing
- Right: overestimates if increasing
- Midpoint: better accuracy
- Trapezoidal: averages left+right
Accuracy
Error decreases as n increases. Trapezoidal error ~ 1/n². Simpson's rule (not shown) achieves 1/n⁴.
Step-by-Step Instructions
- 1Select a function.
- 2Set lower bound a.
- 3Set upper bound b.
- 4Choose number of rectangles.
- 5Compare methods.