   Chapter 5.2, Problem 29E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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 as a limit of Riemann sums.

Explanation

Given information:

The integral function is 134+x2dx

Calculation:

Applytheorem 4

abf(x)dx=limni=1nf(xi)Δx (1)

Calculate the width (Δx) using the relation:

Δx=ban

Substitute 3 for b and 1 for a.

Δx=ban=31n=2n

Calculate xi using the relation:

xi=a+iΔx

Substitute 1 for a and 2n for Δx.

xi=a+iΔx=1+i(2n)

Write the integral function using Equation (1) as follows:

abf(x)dx=134+x2dx

Get f(x)=4+x2

Substitute xi for x.

f(xi)=4+xi2 (2)

Calculate f(xi) using the Equation (2).

Substitute [1+i(2n)] for xi in Equation (2).

f(xi)=4+xi2=4+(1+i(2n))2

Calculate 134+x2dx using Equation (1)

### 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 