# Riemann sum question, with picture

• yeahyeah<3
In summary, the conversation discusses a possible Riemann sum problem, in which 1/n represents the width of the intervals and the sum in brackets relates to the heights of the rectangles. The limits of integration are determined to be 0 and 3, with the integrand being x^2. The individual providing the solution is unsure how to continue due to limited knowledge on the topic.
yeahyeah<3

## Homework Statement

http://img4.imageshack.us/img4/898/integerqj5.jpg

## The Attempt at a Solution

It does appear to be a Riemann sum, I figured the 1/n is probably the width of the intervals and the sum in brackets is related to the sums of the heights of the rectangles. But my class didn't spend much time on Riemann sum's so I'm not sure I know how to continue.

Last edited by a moderator:
Yes, 1/n is the width of the intervals which means that x= x0+ i/n for i= 0, 1, ..., to (x1- x0)n. So it looks like we have f(x0+ i/n)= (i/n)^2 and i is running from 0 to 3n. Looks to me like the limits of integration are 0 and 3 and the integrand is x2.

## 1. What is a Riemann sum?

A Riemann sum is a mathematical concept used to approximate the area under a curve by dividing it into smaller rectangles or trapezoids.

## 2. How is a Riemann sum calculated?

A Riemann sum is calculated by adding up the areas of all the rectangles or trapezoids that make up the approximation. This is typically done by multiplying the width of each shape by its height and then adding all the results together.

## 3. What is the purpose of using a Riemann sum?

The purpose of using a Riemann sum is to estimate the area under a curve, which can be useful in many scientific and mathematical applications. It allows us to find an approximate solution when an exact solution is not possible.

## 4. How accurate is a Riemann sum?

The accuracy of a Riemann sum depends on the number of rectangles or trapezoids used in the approximation. The more shapes used, the closer the approximation will be to the actual area under the curve.

## 5. Can a Riemann sum be used for any type of curve?

Yes, a Riemann sum can be used for any type of curve, as long as it can be divided into smaller shapes for approximation. This includes both continuous and discontinuous curves.

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