34. Arc length for a line Consider the segment of the line y = mx + c on the interval [a, b]. Use the arc length formula to show that the length of the line segment is (b-a)√1 + m². Verify this result by computing the length of the line segment using the distance formula.
34. Arc length for a line Consider the segment of the line y = mx + c on the interval [a, b]. Use the arc length formula to show that the length of the line segment is (b-a)√1 + m². Verify this result by computing the length of the line segment using the distance formula.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I am stuck on the second part verying arc length with the distance formula. plz dont oversimplifed the steps. Thank you for your time.
![34. Arc length for a line Consider the segment of the line y = mx + c on the interval [a, b]. Use the arc length formula to
show that the length of the line segment is (b-a)√1 + m². Verify this result by computing the length of the line segment
using the distance formula.
Constant
f(x) = mx+c²
f'(x) = (1) mx ² + 0 = m
£= So √₁+(m)² dx
2
1+
=
b
Să √i+m² dx
Ji+m² Sa dx
Пате
b
= √₁+ m² (x) | 0
a
L = √√₁+ m²(b=2₂)
L = (b-a) √1+m²
slope
y = mx + c
matc
= 9₂-9₁
X2-X1
t
a
-intrupt
b
y=mx+c
mb+c
2
Distance = √√√(x₂-x₁) + (~3₂-9₁)
2
2
D
9 = (b-a³² + (mb-ma) ²
= √
2
(b-a)² + m² (b-a) ²
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3073de58-1b40-421a-8538-3fd557e8e327%2F25d7391b-f4d8-4644-8470-804fbd029612%2Fpy8r2zp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:34. Arc length for a line Consider the segment of the line y = mx + c on the interval [a, b]. Use the arc length formula to
show that the length of the line segment is (b-a)√1 + m². Verify this result by computing the length of the line segment
using the distance formula.
Constant
f(x) = mx+c²
f'(x) = (1) mx ² + 0 = m
£= So √₁+(m)² dx
2
1+
=
b
Să √i+m² dx
Ji+m² Sa dx
Пате
b
= √₁+ m² (x) | 0
a
L = √√₁+ m²(b=2₂)
L = (b-a) √1+m²
slope
y = mx + c
matc
= 9₂-9₁
X2-X1
t
a
-intrupt
b
y=mx+c
mb+c
2
Distance = √√√(x₂-x₁) + (~3₂-9₁)
2
2
D
9 = (b-a³² + (mb-ma) ²
= √
2
(b-a)² + m² (b-a) ²
2
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