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. D…

09:51

Question

Answered step-by-step

Problem 6 Easy 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.

$ y = \sin x $ , $ y = x $ , $ x = \frac{\pi}{2} $ , $ x = \pi $


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.
MM

Michael M.

May 13, 2021

these are not the right questions that match the book

Top Calculus 2 / BC Educators
Grace He
Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

06:16

Sketch the region enclosed…

02:32

Sketch the region enclosed…

05:13

Sketch the region enclosed…

05:14

Sketch the region enclosed…

01:25

Sketch the region enclosed…

02:53

Sketch the region enclosed…

09:51

Sketch the region enclosed…

06:31

Sketch the region enclosed…

02:31

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

Okay, so we need to draw those given curves. First, let's draw x y axis and then draw the first curve which is 6 okay. So, let's draw sine x, we start from negative pi. This goes to 0 and stop at pi. Then we draw i equals to x, which is something like this: it's like the tangent curve of sine x at the region and x equals to pi over 2 here x equals to pi over 2. This is 1. Sin x equals to 1 point. So here there will be 1 and this is x, equals to pi. Okay, so for the bounded region will be this shaded region right here, so our job is evaluate this area. So how do we do it? We find the approximating, since everything we can see here is represented by x. So when we do the integral we do it with respect to x, okay area, where equals to the integral, with respect to x, all right. So if i so good and we need to find the boundary the boundary for x is just goes from pi over 2 pi, and this here is just upper curve minus the lower curve. Before that we can see, we can draw a typical approximating rectangle, something like this. It'S very small here, if they do me do out, it will look like this is approximating rectangle of the will be delta, x and height will be x. I minus sine x. I okay, so in other words our integral will be x, minus sine x. Okay, then they milorade this integral to find the area of the region. The anti derivative of this is the learned, half x square and sine x. Anti derivative of this is negative cosine. I be plus cosine x, i i plus cosine x. Then we evaluate at x equals pi minus x equal to pi over 2, so the first term there will be pi square over 2 and second, a cosine, pi yo, know cosine. We know cosiniative 1. So this is minus 1 minus x equals to pi over 2, so this will be pi squared over 4 times 1 half is pi square over 8 and cosine pi over 2 is 0, so this plus 0 p, in other words our area. There will be pi square over 2 minus pi square over 8, which is 3 pi square over 8 minus 1 point: okay,

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
177
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Recommended Videos

06:16

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

02:32

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

05:13

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

05:14

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

01:25

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…

09:51

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…

02:31

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

00:33

Write coefficient of x^2 in x^4 +7x^3 + 9x^2 + 11

03:40

Expand a. (x + 2y + 4z)^2 b. (2x – y + z )^2

01:09

Simplify : 101.13 – [36.7 + {13.5 ÷ (3 x 0.5)}] write in copy

01:41

find the square root of 3969 by the division method ?

01:03

Plot the points A(4, 3) and B(-1, 2) on the cartesian plane.

01:46

1. Estimate the quotient: (i) 1010 ÷ 25 (ii) 4295 ÷ 7 (v) 4423 ÷ 21 (vi) 928…

01:27

1. Rao bought notebooks at the rate of 4 for ₹35 and sold them at the rate o…

01:22

1. The local bus service has 2 lines of buses that start together at 8 am. B…

01:04

Three friends start a business and decide to split the profits equally. Susa…

00:55

write true or false root 4 + root 5 equals to root 9

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