When we want to solve the integral using the method of partial fractions, we first factor the denominator x5 - 2x³ - 2x² – 3x − 2 = (x − 2)(x² + 1)(x + 1)², - and then split it into simpler fractions. Which of the following partial fractions decompositions is correct? Pick ONE of these answers (no need to evaluate the integral): 3x²+7x-12 A B C D + + + (x-2)(x²+1)(x+1)² x-2 x²+1 x+1 (x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² 3x² +7x-12 (x-2)(x²+1)(x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² = = 3x² + 7x- 12 x5 - 2x³ 2x²3x2 = = = x-2 A x-2 + A x-2 + Bx+C D + x²+1 (x+1)² A B + x-2 x²+1 + Bx+C x²+1 Bx+C x² +1 + + D x+1 + C (x+1)² -dx + + E (x+1)² D Ex+F x+1 (x+1)² 3x²+7x-12 A B с Dx+E + + + (x-2)(x²+1)(x+1)² x-2 2²+1 x+1 (x+1)²
When we want to solve the integral using the method of partial fractions, we first factor the denominator x5 - 2x³ - 2x² – 3x − 2 = (x − 2)(x² + 1)(x + 1)², - and then split it into simpler fractions. Which of the following partial fractions decompositions is correct? Pick ONE of these answers (no need to evaluate the integral): 3x²+7x-12 A B C D + + + (x-2)(x²+1)(x+1)² x-2 x²+1 x+1 (x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² 3x² +7x-12 (x-2)(x²+1)(x+1)² 3x²+7x-12 (x-2)(x²+1)(x+1)² = = 3x² + 7x- 12 x5 - 2x³ 2x²3x2 = = = x-2 A x-2 + A x-2 + Bx+C D + x²+1 (x+1)² A B + x-2 x²+1 + Bx+C x²+1 Bx+C x² +1 + + D x+1 + C (x+1)² -dx + + E (x+1)² D Ex+F x+1 (x+1)² 3x²+7x-12 A B с Dx+E + + + (x-2)(x²+1)(x+1)² x-2 2²+1 x+1 (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...
Related questions
Question
Transcribed Image Text:When we want to solve the integral
S
using the method of partial fractions, we first factor the denominator
x5 – 2x³ – 2x² – 3x − 2 = (x − 2)(x² + 1)(x + 1)²,
- -
-
and then split it into simpler fractions. Which of the following partial fractions
decompositions is correct?
Pick ONE of these answers (no need to evaluate the integral):
+
3x²+7x-12
A
(x-2)(x²+1)(x+1)² x-2
3x² +7x-12
(x-2)(x²+1)(x+1)²
3x²+7x-12
(x-2)(x²+1) (x+1)²
3x² +7x-12
(x-2)(x²+1)(x+1)²
3x²+7x-12
(x-2) (x²+1)(x+1)²
3x²+7x-12
(x-2)(x²+1)(x+1)²
=
=
3x² + 7x - 12
x5 - 2x³ 2x² 3x - 2
=
=
=
X- -2
A
x-2
A
x-2
A
x-2
A
X- -2
+
+
+
+
+
+
B
x²+1
Bx+C
x²+1
Bx+C
D
+
x² +1 (x+1)²
B
x² +1
+
Bx+C
x² +1
C
x+1
+
+
с
(x+1)²
D
E
+
x+1 (x+1)²
D
(x+1)²
B
с
+
2²+1 x+1
-dx
D
Ex+F
+ +
x+1 (x+1)²
+
Dx+E
(x+1)²
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning