2x – x3 da. = |- In(x – 1) + | Ftan-1(x)| + с Given: + J (x – 1)²(x² + 1)' 2(х-1) 2 2x – x3 determine whether dx converges. If it converges, find its value. (x – 1)² (x² + 1)
2x – x3 da. = |- In(x – 1) + | Ftan-1(x)| + с Given: + J (x – 1)²(x² + 1)' 2(х-1) 2 2x – x3 determine whether dx converges. If it converges, find its value. (x – 1)² (x² + 1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 22E
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![Use these definitions for guide:
Definition 1.6.1. Let a, b, c € R.
1. If f is continuous on [a, +∞), then the improper integral of f over [a, +∞) is defined as
| f(x) dr = ,lim
f(x) dr.
t+00
2. If f is continuous on (-∞, b], then the improper integral of f over (-∞, b] is defined as
| S(x) dr = , lim
f(r) dr.
t-00
The above equalities hold provided the limits exist. In which case, the improper integrals are
said to be convergent. If the limits do not exist, the corresponding integrals are said to be
divergent.
3. If f is continuous on R, then the improper integral of f over (-∞, +∞) is defined as
S(2) dr +
provided that both ſ f(x) dx and * f(x) dx are convergent. If at least one of the
improper integrals on the right-hand side is divergent, then the improper integral on the
left-hand side is divergent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72f6b5b8-edfc-419b-9574-0ca637d88496%2F23c3ca1e-652b-41a3-ab7c-c1854dbe01ca%2Fole9qd5_processed.png&w=3840&q=75)
Transcribed Image Text:Use these definitions for guide:
Definition 1.6.1. Let a, b, c € R.
1. If f is continuous on [a, +∞), then the improper integral of f over [a, +∞) is defined as
| f(x) dr = ,lim
f(x) dr.
t+00
2. If f is continuous on (-∞, b], then the improper integral of f over (-∞, b] is defined as
| S(x) dr = , lim
f(r) dr.
t-00
The above equalities hold provided the limits exist. In which case, the improper integrals are
said to be convergent. If the limits do not exist, the corresponding integrals are said to be
divergent.
3. If f is continuous on R, then the improper integral of f over (-∞, +∞) is defined as
S(2) dr +
provided that both ſ f(x) dx and * f(x) dx are convergent. If at least one of the
improper integrals on the right-hand side is divergent, then the improper integral on the
left-hand side is divergent.
![QUESTION:
2x – a3
dæ. = |- In(x – 1) +
+ tan-1(x)] + C
1
Given:
(х — 1)2(г? +1)
2(х-1)
2
2x – x3
determine whether
-dx converges. If it converges, find its value.
(x – 1)² (x² + 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72f6b5b8-edfc-419b-9574-0ca637d88496%2F23c3ca1e-652b-41a3-ab7c-c1854dbe01ca%2F8uzfya_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION:
2x – a3
dæ. = |- In(x – 1) +
+ tan-1(x)] + C
1
Given:
(х — 1)2(г? +1)
2(х-1)
2
2x – x3
determine whether
-dx converges. If it converges, find its value.
(x – 1)² (x² + 1)
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