Riemann Sum Calculator
Approximate the integral of x^n over an interval using a left Riemann sum with n rectangles.
Exact Val
0.333333
Rect Width0.100000
Error Est0.050000
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.
Example Calculation
Approximate the integral of x² from 0 to 1 with 10 rectangles.
- 01Δx = (1-0)/10 = 0.1
- 02Left endpoints: 0, 0.1, 0.2, ..., 0.9
- 03Sum = (0² + 0.1² + 0.2² + ... + 0.9²) × 0.1
- 04Exact value = 1³/3 = 0.333333...
Frequently Asked Questions
Learn More
How to Calculate Percentages - Complete Guide
Learn how to calculate percentages step by step. Covers finding a percentage of a number, percentage change, reverse percentages, and real-world applications.