Riemann Sum Calculator

Function f(x):

Lower Bound (a):

Upper Bound (b):

Number of Partitions (n):

Method:

What is a Riemann Sum?

A Riemann sum is a mathematical method for approximating the definite integral of a function by dividing the interval into smaller subintervals and calculating the sum of the areas of rectangles that approximate the region under the curve. This technique is fundamental in calculus and provides a concrete way to understand the concept of definite integrals.

How to Calculate Riemann Sums

Step 1

Enter your function in the input field using standard mathematical notation (e.g., x^2 for x², sqrt(x) for square root).

Step 2

Specify the integration bounds by entering the lower (a) and upper (b) limits of integration.

Step 3

Choose the number of partitions (n) to determine the accuracy of the approximation. More partitions generally yield more accurate results.

Step 4

Select your preferred approximation method: – Left Endpoint: Uses function values at left endpoints – Right Endpoint: Uses function values at right endpoints – Midpoint: Uses function values at interval midpoints – Trapezoidal: Averages left and right endpoints

Step 5

Review the calculated result and the step-by-step explanation provided below the calculation.