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

Use Definition 2 to find an expression for the ar…

03:45

Question

Answered step-by-step

Problem 22 Easy Difficulty

Use Definition 2 to find an expression for the area under the graph of $ f $ as a limit. Do not evaluate the limit.

$ f(x) = x^2 + \sqrt{1 + 2x}, \hspace{5mm} 4 \le x \le 7 $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Ma. Theresa Alin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

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

More Answers

01:36

Frank Lin

00:47

Amrita Bhasin

05:45

Linda Hand

01:31

Carson Merrill

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.
ak

Abdulaziz K.

September 13, 2021

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

ON

Olivera N.

November 3, 2020

why is it 9??

SA

Sharieleen A.

October 27, 2020

This will help a lot with my midterm

CA

Catherine A.

October 27, 2020

I've been struggling with Calculus: Early Transcendentals, this is so helpful

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

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

Use Definition 2 to find a…

0:00

Use Definition 2 to find a…

02:49

Use Definition 2 to find a…

05:08

Use Definition 2 to find a…

02:22

Use Definition 2 to find a…

03:45

Use Definition 2 to find a…

02:01

Use Definition 2 to find a…

02:03

$15-17$ Use Definition 2 t…

02:15

Use Definition 2 to find a…

02:01

$17-19$ Use Definition 2 t…

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

for this problem, we need to find an expression for the area under the graph of F of X, which is equal to X squared plus the square root of one plus two X over the interval 47 as a limit. And using only definition to a definition to states that the area this is equal to the limit is and approaches infinity of delta X times is a mission I from one to end of F of X sub I where delta X is just the difference between the end points A and B. So that's B minus A over the number of sub intervals. In now we let except by be right endpoints of these sub intervals. Then if A is the left most endpoint we have except by this is equal to A plus I times delta X. And so we write area equal to limit as N approaches infinity of delta X times information I from one to end of F of a plus delta X times I. Now, if f of X is X squared plus the square root of one plus two X over the interval 47 then we have, you say delta X. This is equal to b minus a over end, which is just seven minus four over and or three over in. And we get area, this is equal to the limit as N approaches infinity of delta X, which is three over in times the summation I from one to end F of a S four plus I times three over in. And so replacing X by four plus I times three over in. We have area which is equal to the limit as an approaches infinity of three over in times it's a mission I from one to end of we have four plus three I over end squared plus the square it of one plus two times four plus three I over. In. And so this is the area in terms of definition to

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
129
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
63
Hosted by: Alonso M
See More

Related Topics

Integrals

Integration

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

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

Use Definition 2 to find an expression for the area under the graph of $ f $ as…

0:00

Use Definition 2 to find an expression for the area under the graph of $ f $ as…

02:49

Use Definition 2 to find an expression for the area under the graph of $f$ as a…

05:08

Use Definition 2 to find an expression for the area under the graph of $f$ as a…

02:22

Use Definition 2 to find an expression for the area under the graph of $ f $ as…

03:45

Use Definition 2 to find an expression for the area under the graph of $ f $ as…

02:01

Use Definition 2 to find an expression for the area under the graph of $f$ as a…

02:03

$15-17$ Use Definition 2 to find an expression for the area under the graph of…

02:15

Use Definition 2 to find an expression for the area under the graph of $f$ as a…

02:01

$17-19$ Use Definition 2 to find an expression for the area under the graph of …
Additional Mathematics Questions

01:19

You can make concrete by mixing 1part cement with 2 parts pea gravel and 3 p…

00:44

using the same ratios, how much cement and how much pea gravel should you us…

12:02

Studies are often done by pharmaceutical companies to determine the effectiv…

01:19

Write the logarithmic equation log7x = y in exponential form.

02:35

Annie is concerned over a report that "a woman over age 40 has a better…

02:01

Annie is concerned over a report that "a woman over age 40 has a better…

01:39

Postpartum depression and anxiety (PPD), is a common medical condition affec…

01:58

A famous designer gave away free perfume samples in the mall, and in 15 minu…

01:58

A famous designer gave away free perfume samples in the mall, and in 15 minu…

02:36

Solve the given problem.
If x​<0, is it ever true that X^-2 < x^-1?…

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