   Chapter 4.2, Problem 7E

Chapter
Section
Textbook Problem

# A table of values of an increasing function f is shown. Use the table to find lower and upper estimates for ∫ 10 30 f ( x ) d x x 10 14 18 22 26 30 f ( x ) − 12 − 6 − 2 1 3 8

To determine

Part (a):

To find:

The lower estimate for 1030f(x)dx

Explanation

1) Concept:

To find the lower estimate by using the formula of the Riemann sum for left end points.

2) Formula:

The Riemann sum for the left endpoints:Ln=i=1nf(xi-1)x

where  x=b - an,n is the number of the subintervals.

3) Given:

4) Calculation:

Since f(x) is increasing,L5  1030fxdx R5.

Here, n=5,a=10 and b=30

So, the width of the subintervals is

x=b-an

x=30-105

x=205=4

Use x=4 to form the subintervals.

10, 14, 14, 18, 18, 22, 22, 26, [26, 30]

Therefore, the left endpoints are x0=10, x1=14, x2=18, x3=22,

To determine

Part (b):

To find:

The upper estimates for 1030f(x)dx

### 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

#### Sketch the graph of y=x24.

Calculus: An Applied Approach (MindTap Course List)

#### Evaluate: a. 2332 b. [(13)3]1/3

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

#### It does not exist.

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: If h'(x) = k(x), then k(x) is an antiderivative of h(x).

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

#### Graph each hyperbola. 4x23y2=36

College Algebra (MindTap Course List) 