Riemann sum question, with picture

Click For Summary
SUMMARY

The discussion focuses on solving a Riemann sum problem related to the function f(x) = x² over the interval [0, 3]. The participant identifies that 1/n represents the width of the intervals and that the sum involves evaluating f(x0 + i/n) where i ranges from 0 to 3n. The conclusion confirms that the limits of integration are indeed 0 and 3, with the integrand being x², which is essential for calculating the definite integral.

PREREQUISITES
  • Understanding of Riemann sums
  • Knowledge of definite integrals
  • Familiarity with the concept of limits in calculus
  • Basic algebra skills for manipulating functions
NEXT STEPS
  • Study the properties of Riemann sums in calculus
  • Learn how to compute definite integrals using the Fundamental Theorem of Calculus
  • Explore the relationship between Riemann sums and the area under curves
  • Practice problems involving integration of polynomial functions
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques and Riemann sums, as well as educators looking for examples to illustrate these concepts.

yeahyeah<3
Messages
27
Reaction score
0

Homework Statement

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

Homework Equations


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:
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 21 ·
Replies
21
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K