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).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6544980f-78eb-42c1-bdf7-a346dd2568f1%2F47126352-e08e-4272-9296-ce667431b246%2F83dxja_processed.png&w=3840&q=75)
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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