Evaluate the line integral by the two following methods. y) dx + (x+y)dy C os counerclockwise around the circle with center the origin and radius 3(a) directly (b) using Green's Theorem.

babeeb0oL 2021-01-15 Answered
Evaluate the line integral by the two following methods. y) dx + (x+y)dy C os counerclockwise around the circle with center the origin and radius 3(a) directly (b) using Green's Theorem.
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Tuthornt
Answered 2021-01-16 Author has 107 answers
Step 1
C(xy)dx+(x+y)dy
C is along a curve
x2+y2=9
x=3cos0
y=3sin0
0 varies from 0 to 2 π
C(3cos03sin0)3sin0d0+(3cos0+3sin0)3cos0d0
C9(cososino+sin20+cos20+cos0sin0)d0
9Cd0
902πd0
92π
=18π
Step 2
Using greens
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