Consider the vector field F(x, y) 3 (х — 2у)і + хуј. Let C denote the curve parametrised by the vector function r(t) = (12 + 2t, t), for 0
Consider the vector field F(x, y) 3 (х — 2у)і + хуј. Let C denote the curve parametrised by the vector function r(t) = (12 + 2t, t), for 0
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:Consider the vector field
F(x, y) = (x – 2y)i+ xyj.
Let C denote the curve parametrised by the vector function
r(t) = (r? + 2t, t),
for 0 <t < 1.
(a) Using the above parametrisation for C, the line integral , F · dr becomes
b
(Pt + Qt² + Rt + S) dt,
where a =
,b =
P =
,Q
,R =
,S=
%3D
%D
а
in lowest terms, where a
b
(b) The value of the line integral can be expressed as the fraction
and
b =
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