   Chapter 4.2, Problem 29E

Chapter
Section
Textbook Problem

# Express the integral as a limit of Riemann sums. Do not evaluate the limit. ∫ 1 3 4 + x 2 d x

To determine

To express:

The integral 134+x2dx as a limit of the Riemann sum but do not evaluate the limit.

Explanation

1) Concept:

Use theorem (4) to express the integral as a limit of the Riemann sum.

Theorem (4):

If f is integrable on [a, b] then

abfxdx=limni=1nfxi x

where x= b - an and xi=a+i x

2) Given:

134+x2dx

3) Calculation:

By comparing the given integral with theorem (4), set

a=1, b=3 and fx=4+x2

Substituting the values of a and b in x.

x= 3-1n

x= 2n

Now, find xi.

xi=a+i x

Substitute a=1 and x= 2n.

xi= 1+2in

So,f(xi)= f1+2in

By using theorem (4),

134+x2dx= limni=1n

### 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

#### Find y and y. y=lnx1+lnx

Single Variable Calculus: Early Transcendentals, Volume I

#### let f(x) = x3 + 5, g(x) = x2 2, and h(x)= 2x + 4. Find the rule for each function. 3. fg

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

#### In Problems 9-20, graph each function. 12.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: The x-intercepts are the values of x for which f(x) = 0.

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 