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

Suppose that $ f(1) = 2 $, $ f(4) = 7 $, $ f^\pri…

View

Question

Answered step-by-step

Problem 70 Hard Difficulty

If $ f(0) = g(0) = 0 $ and $ f^n $ and $ g^n $ are continuous, show that
$$ \int_0^a f(x) g^{\prime\prime} (x) dx = f(a)g^\prime(a) - f^\prime(a)g(a) + \int_0^a f^{\prime\prime} (x) g(x) dx $$


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

WZ
Wen Zheng
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Wen Zheng

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 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
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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

01:48

If $f(0)=g(0)=0$ and $f^{\…

05:17

If $f(0)=g(0)=0$ and $f^{\…

0:00

If f (0) = g(0) = 0 and f&…

02:22

Show that if $f$ and $g$ a…

04:29

Let f be continuous and g …

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

This problem is, if f 0 is equal to g 0 is equal to 0 and f to power, and g to power are continuous, show that, integral from 0 to a f times g prime ram dx is equal to f g r, minus f. Prime g s point plus the integral from 0 to a prime prime times g d. For this problem we can't use integration by parts the forener is integral from a to b. U, o d is equal to? U v from a to b minus integral frontin 8 b prim with the ax now for our problem. We can let? U is equal to f of x and the prim is equal to j f. Primpin prom is equal to f prime of x, and v is equal to 2 prim x, so now its integral integral from 0 to a times, g prim prim dx is equal to f g prime from 0 to a minus, integral f prime prime. This is prime d, prime from 0 to 8 d x, so this is equal to a prime, a minus f. 0, since f 0 is 0. So this is minus point and then minus for this integral. We can also use integration by parts. What? U is equal to f, prom and v. Prime is equal to g prime. Then. U, prime, is equal to i, prime prime and v is equal to g. Then this integral is equal to f prime g from 0 to 8 minus the integral from 0 to a pompom times g. So this is equal to f a g prime, a minus. So when we plug in a and 0 to spring, we have. This is f. Prime, a times g a and things g 0 is 0, so this is 0 and the 10 plus integral from 0 to a a prim prim g dthis is just the same way this. So we have proved this equation.

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
63
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
42
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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

01:48

If $f(0)=g(0)=0$ and $f^{\prime \prime}$ and $g^{\prime \prime}$ are continuous…

05:17

If $f(0)=g(0)=0$ and $f^{\prime \prime}$ and $g^{\prime \prime}$ are continuous…

0:00

If f (0) = g(0) = 0 and f", g"are continuous, show that Z a0f (x)g"(x)dx = f (…

02:22

Show that if $f$ and $g$ are continuous functions, then $$ \int_{0}^{t} f(t-x) …

04:29

Let f be continuous and g be differentiable. If g is even, prove that
Additional Mathematics Questions

02:00

'123455667789
Classify the study as either descriptive or inferentia…

03:47

"2 Earning Money: Marcus works at an ice cream shop He earns $10.50 eac…

04:30

'Empirical rule
You might need: Calculator
The lifespans of tiger…

10:07

"What is the sum of the percentages?
Worksheet 6 Frequency Distrib…

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