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

Evaluate the integral. $ \displaystyle \int_1^…
04:48

Question

Answered step-by-step

Problem 29 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int_0^\pi x \sin x \cos x dx $

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

03:24

WZ

Wen Zheng

Related Courses

Calculus 2 / BC
Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53
Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.
Video Thumbnail

27:53
Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
Join Course
Recommended Videos

0:00

Evaluate the integral.

…

03:59

Evaluate the integral.
…

01:40

Evaluate the integral.
…

04:14

Evaluate the integral.
…

01:03

Evaluate the integral.

02:43

Evaluate the integral.

…

Watch More Solved Questions in Chapter 7

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

Video Transcript

to evaluate the definite integral from 0 to Pi of X times Sine of X times Cosine of X. Dx. We know that sign of two X. This is equal to to sign up X times Cosine of X. And so 1/2 sine of two x. This is just sine of X times go sign of X. Therefore we can read our integral into the integral from 0 to Pi. Ah X times 1/2. sign up two X. Dx and we can Right the constant out. We have 1/2 Integral from 0 to Pi of X times sine of two X dx. From here we want to apply integration by parts. We let U equal to X. And DV Sign of two x. DX so that the U. S. D. X. And we would be Negative co sign of two x over two. So from here we have one half times U times V. That's negative x times go sign up to X over two minus the integral of V times do you? That's negative co sign of two X. Over to the X. Simplifying that we have one half times negative X times go Sign up to X over two Plus we have 1/2 integral of course and have two X. That's just sign of two X over two. And this will be evaluated from zero to pi. And so from here we have negative X. Co sign up to X over four Plus sign of two x Over eight. This evaluated from 0 to Pi And if excess spy we have negative pi close enough to buy Over four plus, sign up to buy over eight. This minus when X0, we have zero Plus sine of 0/8. This is just zero and so we have also. This one is zero and co sign of two pi is one. So the value of the integral would be Negative by over four.

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
71
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
49
Hosted by: Alonso M
See More

Related Topics

Integration Techniques
Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53
Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.
Video Thumbnail

27:53
Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
Join Course
Recommended Videos

0:00

Evaluate the integral. $ \displaystyle \int_0^\pi x \sin x \cos x dx $

03:59

Evaluate the integral. $\int_{0}^{\pi} x \sin x \cos x d x$

01:40

Evaluate the integral. $$\int_{0}^{\pi} \cos x e^{\sin x} d x$$

04:14

Evaluate the integral. $$ \int_{0}^{\pi}(x+x \cos x) d x $$

01:03

Evaluate the integral. $ \displaystyle \int^{\pi}_0 f(x) \,dx $ wher…

02:43

Evaluate the integral. $ \displaystyle \int_0^{\frac{1}{2}} x \cos \pi x dx $
Additional Mathematics Questions

01:49

Let X = the number of nonzero digits in a randomly selected zip
code from…

02:47


Suppose that the cost of drilling x meters for an oil well is
of C = …

01:15

Which of the following statements are correct?
Group of answer choices

02:08

Matthew borrows $200, agreeing to pay it back with a 6% annual
interest a…

02:26

A normally distributed process has specifications of LSL = 75
and USL = 8…

04:13

73% of owned dogs in the United States are spayed or neutered.
Round your…

04:22

When a car slams on its brakes and starts to skid, it leaves
skid marks o…

04:06

A medical researcher obtained a simple random sample of 108
adults in a s…

02:12

Compute the mean and variance of the following probability
distribution.<…

01:36

Thirty percent of all undergraduates at a university are
chemistry majors…

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