Let CCRn Show that 10² F.dr be a curve with continuously differentiable parametrization r: [0, 1] → C. -Jo [F == F. dr. Here, C_ is the same curve as C, but parameterized in the opposite direction by the formula r_(t) = r(1 – t). Hint: Appropriate variable exchange on the left side. Here F · dr = F(r(t)) · r' (t) dt

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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Let CCRn
Ꭱ be a curve with continuously differentiable parametrization r: [0, 1] → C.
Show that
F.dr
=
-[F
F. dr.
C_
Here, C_ is the same curve as C, but parameterized in the opposite direction by the formula
r_(t) = r(1 – t).
Hint: Appropriate variable exchange on the left side. Here
F. dr = F(r(t)). r' (t) dt
Transcribed Image Text:Let CCRn Ꭱ be a curve with continuously differentiable parametrization r: [0, 1] → C. Show that F.dr = -[F F. dr. C_ Here, C_ is the same curve as C, but parameterized in the opposite direction by the formula r_(t) = r(1 – t). Hint: Appropriate variable exchange on the left side. Here F. dr = F(r(t)). r' (t) dt
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