Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1). (a) Find a vector parametric equation (t) for the line segment C so that points P and Q correspond to t = 0 and t = 1, respectively. r(t) (b) Using the parametrization in part (a), the line integral of Falong Cis * = [ * F (F(t)) · 7 ' (t) dt = [" Jo with limits of integration a = F.dr = (c) Evaluate the line integral in part (b). and b = dt
Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1). (a) Find a vector parametric equation (t) for the line segment C so that points P and Q correspond to t = 0 and t = 1, respectively. r(t) (b) Using the parametrization in part (a), the line integral of Falong Cis * = [ * F (F(t)) · 7 ' (t) dt = [" Jo with limits of integration a = F.dr = (c) Evaluate the line integral in part (b). and b = dt
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:Suppose F(x, y) = x² + y²j and C' is the line segment segment from point P = (-3, -4) to Q = (−3, 1).
(a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond to t = 0 and t = 1, respectively.
r(t) =
=
(b) Using the parametrization in part (a), the line integral of Falong Cis
ob
b
[ F · dř = [ * F (F(t)) · 7²' (t) dt =
.
F'
with limits of integration a=
(c) Evaluate the line integral in part (b).
a
and b
=
dt
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