EXAMPLE 4 Find the arc length for the curve y = 2x2 In(x) taking Po(1, 2) as the starting point. 16 If f(x) = 2x2 - In(x), then 16 SOLUTION f'(x) 1 + [F'(x)]? = 1 + = 1 + 16x2 0.5 + = 16x2 + 0.5 + 2 (1 + [F'(x)]² Thus the arc length is given by s(x) V1 + [f'(t)]²? dt dt %3D For instance, the arc length along the curve from (1, 2) to (4, f(4)) is 1 s(4) = + In(4) – 2 16 In(4) + 16 (rounded to four decimal places).
EXAMPLE 4 Find the arc length for the curve y = 2x2 In(x) taking Po(1, 2) as the starting point. 16 If f(x) = 2x2 - In(x), then 16 SOLUTION f'(x) 1 + [F'(x)]? = 1 + = 1 + 16x2 0.5 + = 16x2 + 0.5 + 2 (1 + [F'(x)]² Thus the arc length is given by s(x) V1 + [f'(t)]²? dt dt %3D For instance, the arc length along the curve from (1, 2) to (4, f(4)) is 1 s(4) = + In(4) – 2 16 In(4) + 16 (rounded to four decimal places).
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...
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Question
![EXAMPLE 4
Find the arc length for the curve y = 2x²
In(x) taking Po(1, 2) as the starting point.
%3D
16
SOLUTION
If f(x) = 2x2
치n(x), then
16
f'(x)
1 + [F'(x)]?
1 +
%3D
= 1 + 16x2 – 0.5 +
16x2 + 0.5 +
1 + [f'(x)]?
Thus the arc length is given by
'VI+ [r'(e)}? dt
s(x)
dt
1
For instance, the arc length along the curve from (1, 2) to (4, f(4)) is
s(4)
+
In(4) – 2
16
In(4)
+
16
(rounded to four decimal places).
II
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e02d31-57b8-4522-b989-9d7821fe7afa%2F98cb4058-21ec-4a9b-8bf0-a147c13f861b%2Fae5cwp8_processed.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 4
Find the arc length for the curve y = 2x²
In(x) taking Po(1, 2) as the starting point.
%3D
16
SOLUTION
If f(x) = 2x2
치n(x), then
16
f'(x)
1 + [F'(x)]?
1 +
%3D
= 1 + 16x2 – 0.5 +
16x2 + 0.5 +
1 + [f'(x)]?
Thus the arc length is given by
'VI+ [r'(e)}? dt
s(x)
dt
1
For instance, the arc length along the curve from (1, 2) to (4, f(4)) is
s(4)
+
In(4) – 2
16
In(4)
+
16
(rounded to four decimal places).
II
II
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