Textbook ExpertVerified Tutor
9 Nov 2021
Given information
We have
and 
be any two antiderivatives of 
on 
.
Step-by-step explanation
Step 1.
Differentiating both the antiderivatives we have the following pair of equations
Therefore
In interval according to Lagrange´s mean value theorem we have atleast one point 
according to Lagrange´s mean value theorem we have atleast one point 
We have from (1)
Τherefore
From (1) we have
Hence antiderivative of 
being 
we get
being we get
where 
is a constant
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- 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 40a
- Problem 40b
- Problem 40c
- Problem 40d
- Problem 41
- Problem 42
- Problem 43a
- Problem 43b
- Problem 43c
- Problem 43d
- Problem 44
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54a
- Problem 54b
- Problem 55a
- Problem 55b
- Problem 55b
- Problem 56
- Problem 57a
- Problem 57b
- Problem 57c
- Problem 57d
- Problem 58a
- Problem 58b
- Problem 58c