Suppose F(x, y) = x² + y² and C is the line segment from point A = (1, -1) to B = (3,-5). (a) Find a vector parametric equation (t) for the line segment C so that points A and B correspond to t = 0 and t = 1, respectively. F(t) = (b) Using the parametrization in part (a), the line integral of along Cis dt [ F · d² = [° F (F(t)) · F' (t) dt = "C with limits of integration a = and b = (c) Evaluate the line integral in part (b).
Suppose F(x, y) = x² + y² and C is the line segment from point A = (1, -1) to B = (3,-5). (a) Find a vector parametric equation (t) for the line segment C so that points A and B correspond to t = 0 and t = 1, respectively. F(t) = (b) Using the parametrization in part (a), the line integral of along Cis dt [ F · d² = [° F (F(t)) · F' (t) dt = "C with limits of integration a = and b = (c) Evaluate the line integral in part (b).
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 + y² and C is the line segment from point A = (1, −1) to B = (3, −5).
(a) Find a vector parametric equation (t) for the line segment C so that points A and B correspond to t= 0 and t = 1, respectively.
F(t) =
=
(b) Using the parametrization in part (a), the line integral of along C' is
dt
LE · dF = [ ° F (F(t)) - 7"' (t) dt = √°
with limits of integration a =
and b =
(c) Evaluate the line integral in part (b).
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