What is Riemann Sums?

Riemann sum is a method used for approximating the definite integral of a function over a given interval by dividing the interval into subintervals and then evaluating the function at specific points within each subinterval. It is named after the German mathematician Bernhard Riemann.

Riemann Sums

Riemann Sum is a certain kind of approximation of an integral by a finite sum. A Riemann sum is the sum of rectangles or trapezoids that approximate vertical slices of the area in question. German mathematician Bernhard Riemann developed the concept of Riemann Sums.

In this article, we will look into the Riemann sums, their approximation, sum notation, and solved examples in detail.

Table of Content

  • What is Riemann Sums?
  • Riemann Approximation
  • Summation Notation of Riemann Sum
  • Examples Using Riemann Sum Formula
  • FAQs on Riemann Sum

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What is Riemann Sums?

Riemann sum is a method used for approximating the definite integral of a function over a given interval by dividing the interval into subintervals and then evaluating the function at specific points within each subinterval. It is named after the German mathematician Bernhard Riemann....

Riemann Approximation

Riemann’s sums are a method for approximating the area under the curve. The intuition behind it is, that if we divide the area into very small rectangles, we can calculate the area of each rectangle and then add them to find the area of the total region. These sums can also be used to approximate and define the definite integrals....

Summation Notation of Riemann Sum

Steps given below should be followed to find the summation notation of the Riemann Integral....

Examples Using Riemann Sum Formula

Example 1: Choose which type of the Riemann integral is shown below in the figure....

FAQs on Riemann Sum

What is the Purpose of Riemann Sums?...