   Chapter 4.2, Problem 20E

Chapter
Section
Textbook Problem

# Express the limit as a definite integral on the given interval. lim n → ∞ ∑ i = 1 n x i * ( x i * ) 2 + 4    △ x ,    [ 1 , 3 ]

To determine

To express:

The limit as a definite integral on the given interval.

Explanation

1) Concept:

Use the theorem (4) to express the limit as a definite integral on the given interval.

2) Theorem (4):

If f is integrable on [a, b] then

abf(x)dx=limni=1nf(xi)x

where

x=b - an and xi=a+i x

3) Given:

limni=1nxi*(xi*)2+4x,  [1, 3]

4) Calculation:

Compare the given sum with the theorem (4), so fx is

fx=xx2+4

Also, it is given that a=1 and b=3

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 7-28, perform the indicated operations and simplify each expression. 15. 4x295x26x+9

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 19-26, find the derivative of each function. 19.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: If f(x) is continuous and decreasing, f(n) = an for all n = 1, 2, 3, …, and

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th 