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

Sketch the region enclosed by the given curves an…

05:48

Question

Answered step-by-step

Problem 12 Medium Difficulty

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to $ x $ and $ y $. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.

$ 4x + y^2 = 12 $ , $ x = y $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

SL
Sky Li
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Sky Li

Numerade Educator

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

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

09:51

Sketch the region enclosed…

04:15

Sketch the region enclosed…

02:53

Sketch the region enclosed…

05:06

Sketch the region enclosed…

06:31

Sketch the region enclosed…

06:31

Sketch the region enclosed…

04:42

Sketch the region enclosed…

Watch More Solved Questions in Chapter 6

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
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61

Video Transcript

So again we need to find Ah ah. We need to draw the curves given curves. And this time, um, it's not very clear The function is real ize It can be represented by X or why so we reform this first formula here and we see we can see the we can't express acts in terms ofthe why very easily. We just moved. Why square to the other side? I'm divided by four. So it will be twelve miners. Weiss. We're over four and ah, this is just ex Pecos way after reformulating we can see that we can say everything is represented bit by Why? So why don't we take the integrate Made the respect Why? All right, um, let's draw the pictures. So here is X Y access. You know, if I draw this, this is a problem. Um, then why he called zero X equal to three. So I just look like this. And a x Pecos to zero. Why he caused Teo tough. So why will Why square very coast twelve. So? Well, he close to, uh, two times Square three and negative. Two times Square three. So this problem will look like this. Okay, and I also got this wiII coast packs It's the street line And I would go those two intersection So this is X coast boy. Um and I miss Ah, no time for this. Do you know this intersection X one here. This intersection is X to here and corresponding x one corresponding to buy one and ah, actual corresponding to bite you since we decided to integrate with respect. Why less fine hour? Why want wide too? All right. Here is the enclosed the region, right? No. You know to find the boy y y too. Ah, you know he should satisfy this equation. Twelve Oh, minus Why square over four Pecos. Why, that's when those two curves intersect. So this will give us with times for on both side and move everything to the right. Give us a boy square Plus for why minus twelve. He called to zero and we can solve this a factor. A factoring So this is a live plus six. Why? Minus two You go to zero and we know why wise the smaller one. So where wass close to ninety six and why to coast to Okay, um and we draw tape approximating or tango since we decided to integrate with respect. Why are right? Tango looks horizontal, right? Say, over typical rectangle goes here If we zoom out there look like this home and here is dealt Why, um the the the heart ofthe this rectangle will be the right carved minus the left curb. So the right curves right now is this whole thing. So you will be twelve, Linus. Why? Hi square over four Mari this y I Okay. They're, uh, next page in to find the area of the shaded regions. I did note as a so are able eco's to the integral with respect to why so have the y at the end and the boundary for why goes from it goes from my one two y two. We know why y's negative sakes and lie to you goes too. So it's goes from ninety six two two and integral in sidings her into grow is just ah, this height off approximating rectangle. Without a subscript it will be Charles minus y square over four minus. Why? No. In the end, he derivative of that will be first Hermes twelve or for his way. So it's three y and a minus Ah, Y square over four. Anti akira tip of that. It will be of why over tough time's white cube minus Why over too. Why square and this evaluated at the bank three hiss. Why comes, too? Yeah, by coast Negative six. This very coast tio y close to this is six miners two Cuba is eight. Eight or twelve is two or three miners. Um, to square, which is for over two is two. Hey, this miners, But plug in white coat tonight of six. This is nineteen. Eighteen, um, minus more over itself. Times negative six Q and minus. But I have times thirty six riches and him. All right, so this really coast Tio, um, let's look at this time first, this cancer is one six. So it's one half. Oh, the negative sign canceled. So this whole term will be positive. Um, Isla have times, so it will be positive. But I have times six square, which is thirty six. So plus on a thirty six divided by choice is placid. Okay, so those eighteen cans old God, this is for minus to third, minus negative. Eighteen. So is class eighty. So this whole thing will be twenty two minus to third. Twenty two minors to third of the sixty six over, three, minus two third. So our answer there will be sixty four over three.

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
83
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
52
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Recommended Videos

09:51

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

04:15

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

02:53

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

05:06

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

06:31

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

06:31

Sketch the region enclosed by the given curves. Decide whether to integrate wit…

04:42

Sketch the region enclosed by the given curves. Decide whether to integrate wit…
Additional Mathematics Questions

05:18

men, 90% of BMIs are below 36.7, and 95% are below 38.9. In women, 90% of BM…

05:30

(28 points, each points) For the following statement, identify the variable(…

01:12

Let Y denote the number of broken eggs in a randomly selected carton of one …

01:51

Baby elk and their chances Biologists estimate that a randomly selected baby…

03:36

Modeling men's heights The distribution of heights of adult American me…

03:18

An arithmetic series has first term of 4 and its 30th term is 1000. Find the…

01:33

Identify the population the parameter, the sample, and the statistic in the …

05:51

Unit 5 Test - Probablllty Distribution
spinner with five regions numbered…

04:16

In a collection of 56 coins, 18 are rare If you select 10 of the coins, one …

03:55

For each of the following_ determine the appropriate level of measurement fo…

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