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

Which of the integrals $ \displaystyle \int^2_1 \…

00:36

Question

Answered step-by-step

Problem 66 Hard Difficulty

Use properties of integrals, together with Exercises 27 and 28, to prove the inequality.

$ \displaystyle \int^{\pi/2}_0 x \sin x \,dx \le \frac{\pi^2}{8} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Bobby Barnes
University of North Texas

Like

Report

Textbook Answer

Official textbook answer

Video by Bobby Barnes

Numerade Educator

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

More Answers

00:53

Frank Lin

00:40

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 2

The Definite Integral

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

Michael Jacobsen

Idaho State University

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

01:48

$61-62$ Use properties of …

0:00

Use properties of integral…

01:06

$65-66$ Use properties of …

00:32

Use properties of integral…

02:22

Use the properties of inte…

02:09

Use the result of Exercise…

00:57

Evaluate the integrals in …

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
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
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75

Video Transcript

So they want us to prove this inequality here, Uh, using what we've done in 27 28. Um, so I'm just gonna write those results down, and we'll just kind of use them. So one thing that we might know, So let's do X sign of X here. Well, the reason why I would think they would want us to look at Exercises 27 28 is because we know that sign of X will always be less than or equal to one. So this here will always be less than or equal to just x times one. And now, since we have this inequality here, if we were to integrate each side, the left side should still be less than the right side. So this is going to be integral of zero two pi, half of x, Sign of X dx lesson opportunity. Integral from zero two pi, half of x dx. And now from number 27 this says, Well, it's just gonna be be square in my sights were all over to Let's go out to do that. So it will be pi squared over four minus zero all over to which is going to be pi squared over eight. So we have shown that this is less than or equal to pi squared or eight. So, um, so you passed your proof saying You love proof box and spotted face because you're glad you're done with it.

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
67
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
43
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

Michael Jacobsen

Idaho State University

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

01:48

$61-62$ Use properties of integrals, together with Exercises 27 and $28,$ to pr…

0:00

Use properties of integrals, together with Exercises 47 and 48 , to prove the i…

01:06

$65-66$ Use properties of integrals, together with Exercises 27 and $28,$ to pr…

00:32

Use properties of integrals, together with Exercises 27 and 28, to prove the in…

02:22

Use the properties of integrals to verify the inequality without evaluating the…

02:09

Use the result of Exercise 27 and the fact that $ \displaystyle \int^{\pi/2}_0 …

00:57

Evaluate the integrals in Exercises 1-28 $\int_{\pi / 2}^{\pi} \frac{\sin 2 x}…
Additional Mathematics Questions

01:06

Find the derivative of the function. y = cos(a6 + x6)

04:17

Locate and classify all the critical points of the function. (Order your ans…

03:15

If the Morgans can afford a monthly amortization payment of?$800 then the 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
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started