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A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0. Assume that 7, B, and h are all C1. (a) Prove that t2 T2 7()|| dt = I }(+)|| dr. (b) Interpret the result geometrically.

A curve joining the points Pi and P2 in R2 is parameterized by two different paths, 7(t); t1 0. Assume that 7, B, and h are all C1. (a) Prove that t2 T2 7()|| dt = I }(+)|| dr. (b) Interpret the result geometrically.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 41E
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A curve joining the points Pı and P2 in R² is parameterized by two different paths, 7(t); t1 <t< t2 and B(T); T1 <T< T2, where T = h(t) and h'(t) > 0. Assume that 7, B, and h are all C1. (a) Prove that •t2 T2 17()|| dt = " 13(-)|| dr. t1 T1 (b) Interpret the result geometrically.
Transcribed Image Text:A curve joining the points Pı and P2 in R² is parameterized by two different paths, 7(t); t1 <t< t2 and B(T); T1 <T< T2, where T = h(t) and h'(t) > 0. Assume that 7, B, and h are all C1. (a) Prove that •t2 T2 17()|| dt = " 13(-)|| dr. t1 T1 (b) Interpret the result geometrically.
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