Solving Calculus Homework: Stuck on #11 Riemann's Sum

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SUMMARY

The discussion centers on solving a calculus homework problem involving Riemann's Sum, specifically for the integral of the function \(x^p\) over the interval from 0 to 2. The user expresses confusion about how to start the problem and has attempted to substitute values for \(p\) without success. Participants suggest clarifying the problem statement and recommend starting with simple cases of \(n = 2, n = 3,\) and \(n = 4\) subintervals to better understand the concept of Riemann sums.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the concept of Riemann sums
  • Basic algebra skills for manipulating functions
  • Knowledge of limits and continuity
NEXT STEPS
  • Study the definition and properties of Riemann sums
  • Practice calculating Riemann sums for various functions
  • Explore the relationship between Riemann sums and definite integrals
  • Learn about the convergence of Riemann sums as \(n\) approaches infinity
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Students studying calculus, particularly those struggling with Riemann sums and integral concepts. This discussion is beneficial for anyone seeking to improve their understanding of how to approach calculus homework problems effectively.

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Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.
 

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KF33 said:

Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.
Could you please show us a) what's written on number 11, as your picture is unreadable without processing it further, and b) what you have done so far and why?
 
Screen Shot 2019-01-24 at 6.04.34 PM.png
 

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Last edited by a moderator:
KF33 said:

Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.

What is the definition of a Riemann sum? For the function ##x^p##, what would be a Riemann sum for ##\int_0^2 x^p \, dx## if you were to divide the interval from ##x=0## to ##x = 2## into ##n## equal-sized subintervals?

To fix in your mind what is going on, try first the simple cases of ##n = 2, n = 3## and ##n = 4## subintervals.
 

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