Cis the polar curve with polar representation r = cos30, 0sesA a) 1 A = F-dr, F= (-y,2), Using this given area formula, Evaluate the area that is enclosed by the polar curve. Hint. You may find the identities cos(at) cos(bt) = (cos((a - b)f) + cos((a + b)f) and cos(at) sin(bt) = (sin((a + b)t - sin((a - b)t)) useful b) Now letting F(x, y) = (4x, 3xy). Use Green's theorem to evaluate the line integral fF. dr. c) 2m Compute the line integral 3 Let C denote the portion of the polar curve C with<0s: f G dr where G(r, y) (e"y,e"). (Hint. Consider the condition that would allow for the simplest computation of the line integral.)
Cis the polar curve with polar representation r = cos30, 0sesA a) 1 A = F-dr, F= (-y,2), Using this given area formula, Evaluate the area that is enclosed by the polar curve. Hint. You may find the identities cos(at) cos(bt) = (cos((a - b)f) + cos((a + b)f) and cos(at) sin(bt) = (sin((a + b)t - sin((a - b)t)) useful b) Now letting F(x, y) = (4x, 3xy). Use Green's theorem to evaluate the line integral fF. dr. c) 2m Compute the line integral 3 Let C denote the portion of the polar curve C with<0s: f G dr where G(r, y) (e"y,e"). (Hint. Consider the condition that would allow for the simplest computation of the line integral.)
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:C is the polar curve with polar representation r = cos30, 0s0sn
个9
a)
A =
F dr, F (-y, x),
Using this given area formula, Evaluate the area that is enclosed by the polar curve. Hint. You
may find the identities
cos(at) cos(bt) = (cos((a - b)t) + cos(a + b)t) and cos(at) sin(bt) = (sin((a + b)t - sin((a - b)t) useful
b)
Now letting F(x, y) = (4x, 3xy). Use Green's theorem to evaluate the line integral fF dr.
c)
27
Let C, denote the portion of the polar curve C with <0<. Compute the line integral
f G dr where G(r, y) = (e"y,e"). (Hint. Consider the condition that would allow for the
simplest computation of the line integral.)
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