Question
Asked Nov 19, 2019
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Evaluate the line integral
2
Cx2y)dx- 2xdy
along each of the following closed paths, taken counterclockwise:
a) the circle x2 y2 1
b) the square with corners at (1,1), -1,1), (-1,-1), (1,-1)
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Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken counterclockwise: a) the circle x2 y2 1 b) the square with corners at (1,1), -1,1), (-1,-1), (1,-1)

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Expert Answer

Step 1

Given that the integral,

φ(r+ 2y) ά -2χν
- 2χ
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φ(r+ 2y) ά -2χν - 2χ

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Step 2

a)The given circle,

=1
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=1

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Step 3

Evaluate the given integral along the above circle in the fo...

x = cos
dr = -sin Ode
and y sin 0 dy cos ede
e will be vary from 0 to 27
Substitute all values in the given integral,
(x+2y)d-2xdy [(cos+2sine)(-sin Ode)-2 cos e cos ede
--cossin -2 sin e)-2cos ede
=Tcos@sin -2ie
0
2#
ofs-R
-2
1
-sin 20 2
2
cos 20
2
2
=-4T
help_outline

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x = cos dr = -sin Ode and y sin 0 dy cos ede e will be vary from 0 to 27 Substitute all values in the given integral, (x+2y)d-2xdy [(cos+2sine)(-sin Ode)-2 cos e cos ede --cossin -2 sin e)-2cos ede =Tcos@sin -2ie 0 2# ofs-R -2 1 -sin 20 2 2 cos 20 2 2 =-4T

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Advanced Math