Riemann Sum Calculator

Approximate definite integrals using Left, Right, Midpoint, or Trapezoidal Riemann sums.

Made by Eric Wang

Input Parameters

Results

Approximated Sum: --

Actual Integral: --

Absolute Error: --

Note: This is an approximation. Actual integral may differ.

Areas per Subinterval

Visualization

Help

How to Use
  • Enter a function in terms of x (e.g., x**2 for x squared).
  • Specify the interval [a, b] and number of subintervals N.
  • Choose the Riemann sum method.
  • Click Calculate to see the approximation and graph.
About Riemann Sums

Riemann sums approximate the area under a curve by dividing the interval into subintervals and summing areas of rectangles or trapezoids.

  • Left: Uses left endpoints of subintervals.
  • Right: Uses right endpoints.
  • Midpoint: Uses midpoints.
  • Trapezoidal: Uses trapezoids for better accuracy.
Supported Functions

You can use the following mathematical functions in your expression:

  • sin(x) or Math.sin(x) - Sine
  • cos(x) or Math.cos(x) - Cosine
  • tan(x) or Math.tan(x) - Tangent
  • exp(x) or Math.exp(x) or e**x - Exponential (e^x)
  • log(x) or Math.log(x) or ln(x) - Natural logarithm
  • sqrt(x) or Math.sqrt(x) - Square root
  • pi or Math.PI - Pi constant
  • e or Math.E - Euler's number
  • Arithmetic operators: +, -, *, /, ** (power)
  • Parentheses for grouping