Consider the curve segments: 1 S1: y = x from x = to x = 2 and 2. %3D S2: y = Väfrom x = to x = 4. Set up integrals that give the arc lengths of the curve segments by integrating with respect to x. Demonstrate a substitution that verifies that these two integrals are equal. Substitution u = 2x made in the integral L2 = |1+dx verifies that the length of the second segment is equal to 4x the length of the first segment: L1 = / V4x + Idx. Substitution u = Vämade in the integral L2 = 1+ dx verifies that the length of the second segment is equal to 2r the length of the first segment: Li = 2x+ Idx.
Consider the curve segments: 1 S1: y = x from x = to x = 2 and 2. %3D S2: y = Väfrom x = to x = 4. Set up integrals that give the arc lengths of the curve segments by integrating with respect to x. Demonstrate a substitution that verifies that these two integrals are equal. Substitution u = 2x made in the integral L2 = |1+dx verifies that the length of the second segment is equal to 4x the length of the first segment: L1 = / V4x + Idx. Substitution u = Vämade in the integral L2 = 1+ dx verifies that the length of the second segment is equal to 2r the length of the first segment: Li = 2x+ Idx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Substitution u = x² made in the integral L2 =
1+dx verifies that the length of the second segment is equal to
the length of the first segment: L1 = / V4x + Idx.
Substitution u = Vi made in the integral L2 =
|1+dx verifies that the length of the second segment is equal to
4x
the length of the first segment: L1 =
| V4x + Idx.
Substitution u = made in the integral L2 =
1 +dx verifies that the length of the second segment is equal to
4x
the length of the first segment: L =
I V4x + Idx.
Transcribed Image Text:Consider the curve segments:
S1: y = x* from x =to x = 2 and
S2: y = Va from x =; to.x = 4.
Set up integrals that give the arc lengths of the curve segments by integrating with respect to x. Demonstrate a substitution that
verifies that these two integrals are equal.
Substitution u = 2x made in the integral L2 =
|1+dx verifies that the length of the second segment is equal to
4x
the length of the first segment: L1 = / V4x + Idx.
Substitution u = Vi made in the integral L2 =
1+
2x
dx verifies that the length of the second segment is equal to
the length of the first segment: L, =
/ V2r + Idx.
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