Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

(a) Estimate the area under the graph of $ f(x) =…

02:56

Question

Answered step-by-step

Problem 2 Medium Difficulty

(a) Use six rectangles to find estimates of each type for the area under the given graph of $ f $ from
$ x = 0 $ to $ x = 12 $.
(i) $ L_{6} $ (sample points are left endpoints)
(ii) $ R_{6} $ (sample points are right endpoints)
(iii) $ M_{6} $ (sample points are midpoints)

(b) Is $ L_{6} $ an underestimate or overestimate of the true area?

(c) Is $ R_{6} $ an underestimate or overestimate of the true area?

(d) Which of the numbers $ L_{6} $, $ R_{6} $, or $ M_{6} $ gives the best estimate? Explain.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Frank Lin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Frank Lin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 1

Areas and Distances

Related Topics

Integrals

Integration

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

Video Thumbnail

40:35

Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

Join Course
Recommended Videos

0:00

(a) Use six rectangles to …

04:56

(a) Use six rectangles to …

03:44

Use six rectangles to find…

01:12

2. a) Use six rectangles t…

02:00

'a. Use six rectangle…

03:23

Estimating an Area Using R…

05:00

Estimating Areas Using Rec…

03:44

(a) Estimate the area unde…

11:01

(a) Estimate the area unde…

01:54

Estimating a Definite Inte…

Watch More Solved Questions in Chapter 5

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32

Video Transcript

so this problem as us to use to use the rectangle message for different simple points to estimate the integral F from zero to twelve or the area. And there's a curse, which means in the group, if you have the tax book, you can see that the function is decreasing concrete down and in each case they ask you to use six rectangles. Therefore, each issue off them will have based too. Ah, base of lens too. And hideaways rectangle depends on the employees on the use. So in the case of the if you want to use the laugh and point than Zen Point will be actually ho zero, two, four, six, eight ten But and each issue off one has ish off them has silenced to a starbase. Therefore, your integral estimate will be like this zero. Plus, they're forced to cool. The last one left one point p f off ten for the meadow M point again each Each of them has a rectangular space too. And the middle Cemal point will be one three, five up to eleven. And I'm sorry, this is a middle cemal point. So this should be past three. And if you want to use the the right symbol point, which is part two. Then the end point will be two for six up to twelve, and you can figure out this value by looking at the crowd from your textbook. So because it's a decreasing functions and laugh and point is higher lands middle point, its hunger in his heart and the Ryan Point. So it's eleven point that's who overestimates area the right hand point Matthews. Because we take the lower one, we're on dress made area and and because is decreasing in the middle, the middle point is closer to the average off F elt That interval compared to the left or right on point, therefore gives up assess Nate.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
151
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Integrals

Integration

Top Calculus 1 / AB Educators
Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

Video Thumbnail

40:35

Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

Join Course
Recommended Videos

0:00

(a) Use six rectangles to find estimates of each type for the area under the gi…

04:56

(a) Use six rectangles to find estimates of each type for the area under the gi…

03:44

Use six rectangles to find estimates of each type for the area under the given…

01:12

2. a) Use six rectangles to find estimates of each type for the area under the…

02:00

'a. Use six rectangles to find estimates of each type for the area under the gi…

03:23

Estimating an Area Using Rectangles. $$ \begin{array}{l}{\text { (a) Use six re…

05:00

Estimating Areas Using Rectangles In these exercises we estimate the area under…

03:44

(a) Estimate the area under the graph of $ f(x) = 1 + x^2 $ from $ x = -1 $ to …

11:01

(a) Estimate the area under the graph of $f(x)=1+x^{2}$ from $x=-1$ to $x=2$ us…

01:54

Estimating a Definite Integral Use the table of values to estimate $$\int_{0}^…
Additional Mathematics Questions

01:51

Question 5 Which of the following are steps in the Independence Awareness Cy…

01:10

LOBAL INDEPENDENCE TRAINING Other Professional Staff
of 11 questions answ…

04:25

Which aspect of an entity and its environment would you most likely obtain a…

00:54

Question 18 of 50 You are entering a Payment at Time of Sale transa…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started