c. The seemingly different answers are the same, because they differ by a constant. In fact, (x + 1)² 22 2 - - 2(x + 1) + ln x + 1| − 2 · − x + ln \x + 1) == 2

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question

I dont understand what they want me to do for part c

#TI
a)
2
Sta
X+1
•
71. Different methods Let I =
2
= $_+² du
u
= Scu-13² du
2
u
S
= Scu-1)(1-1) du
(-۱
u
S
a. Evaluate / using the substitution u = x + 1.
b. Evaluate / after first performing long division on the integrand.
c. Reconcile the results in parts (a) and (b).
dx
u²²-u-u+1 du
u
2
2
u
u-2u+1 du
u
u
S#1
x + 1
2u + 1 dx
u-2 + 1 dx
M = x + 1 x= μ-1
du = dx
2
= μ² - 2u + ln /u/+C
2
- dx.
2
= (x+1) - 2 (x+1) + ln (x+1)+c
2
s dx
b) X
2
X+1
X+1
X-1
x²
x + x
- X
-x+1
Seit
I
I dx
de
+-
X+1
= Sxdx + S-idx + S ____ dx
X+1
2
x -x + ln | X + 1 | + c
2
2
(X+ 1)² - 2 (X+1) + ln (x+1) - ( 22 −X + ln | X + ¹ \ )
2
Transcribed Image Text:#TI a) 2 Sta X+1 • 71. Different methods Let I = 2 = $_+² du u = Scu-13² du 2 u S = Scu-1)(1-1) du (-۱ u S a. Evaluate / using the substitution u = x + 1. b. Evaluate / after first performing long division on the integrand. c. Reconcile the results in parts (a) and (b). dx u²²-u-u+1 du u 2 2 u u-2u+1 du u u S#1 x + 1 2u + 1 dx u-2 + 1 dx M = x + 1 x= μ-1 du = dx 2 = μ² - 2u + ln /u/+C 2 - dx. 2 = (x+1) - 2 (x+1) + ln (x+1)+c 2 s dx b) X 2 X+1 X+1 X-1 x² x + x - X -x+1 Seit I I dx de +- X+1 = Sxdx + S-idx + S ____ dx X+1 2 x -x + ln | X + 1 | + c 2 2 (X+ 1)² - 2 (X+1) + ln (x+1) - ( 22 −X + ln | X + ¹ \ ) 2
c. The seemingly different answers are the same, because they differ by a constant. In fact,
(x + 1)²
X
3
2(x + 1) + ln |x + 1| − (22²2 - x + ln x + 1|
+11)
2
2
=
Transcribed Image Text:c. The seemingly different answers are the same, because they differ by a constant. In fact, (x + 1)² X 3 2(x + 1) + ln |x + 1| − (22²2 - x + ln x + 1| +11) 2 2 =
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning