Riemann Sum Calculator

About the Riemann Sum Calculator

The Riemann Sum Calculator computes the Riemann sum for a function f(x) over an interval [a, b] with n subintervals, using left, right, or midpoint methods. It supports simple functions like x^2, sin(x), cos(x), e^x, and ln(x). This tool is ideal for calculus students, teachers, and professionals.

• Features:
  • Computes Riemann sums using left, right, or midpoint methods.
  • Supports polynomials (e.g., x^2), trigonometric functions (sin, cos), exponentials (e^x), and logarithms (ln).
  • Keypad for easy input with digits, variable (x), operators (+, -, *, /, ^), and functions (sin, cos, ln, e^).
  • Clear and backspace functionality, with a "Copy" button for results.
• Practical Applications: Useful in calculus for approximating definite integrals and understanding area under curves.
• How to Use
  • Enter a function (e.g., x^2).
  • Enter the interval [a, b] (e.g., 0; 4).
  • Enter the number of subintervals (e.g., 100).
  • Select the method (left, right, or midpoint).
  • Use the keypad to insert digits, variable (x), operators, and functions.
  • Click "Calc" to compute the Riemann sum and view the result, then use "Copy" to copy the result.
  • Use "Clear" to reset, or "⌫" to delete the last character.
  • Share or embed the calculator using the action buttons.
• Helpful Tips
  • Ensure the function is defined on [a, b] (e.g., avoid ln(x) for x ≤ 0).
  • Ensure a < b for the interval.
  • Use a positive integer for the number of subintervals.
  • Use * for multiplication and / for division in complex expressions (e.g., sin(x)/x).
  • Larger n values improve accuracy but increase computation time.
• Examples
  • Example 1: Polynomial: Riemann sum for f(x) = x^2 on [0, 2], n = 100, midpoint method
    • Input: Function: x^2, Interval: 0; 2, Subintervals: 100, Method: Midpoint
    • Steps: Δx = (2-0)/100 = 0.02, sum f(x_i + Δx/2) * Δx for i = 0 to 99.
    • Result: Riemann sum ≈ 2.6667 (close to ∫x^2 dx = 8/3)
  • Example 2: Trigonometric: Riemann sum for f(x) = sin(x) on [0, π], n = 50, right method
    • Input: Function: sin(x), Interval: 0; 3.14159, Subintervals: 50, Method: Right
    • Steps: Δx = (π-0)/50 ≈ 0.06283, sum f(0 + i*Δx) * Δx for i = 1 to 50.
    • Result: Riemann sum ≈ 2.0000 (close to ∫sin(x) dx = 2)
  • Example 3: Exponential: Riemann sum for f(x) = e^x on [0, 1], n = 100, left method
    • Input: Function: e^x, Interval: 0; 1, Subintervals: 100, Method: Left
    • Steps: Δx = (1-0)/100 = 0.01, sum f(0 + i*Δx) * Δx for i = 0 to 99.
    • Result: Riemann sum ≈ 1.7083 (close to ∫e^x dx = e-1 ≈ 1.7183)

Calculate Riemann sums with ease using this Riemann Sum Calculator. Share or embed it on your site!