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

babeeb0oL

Answered question

2021-01-15

Using the two approaches below, evaluate the line integral. 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.

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-01-16Added 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Multivariable calculus

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?