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Problem using Green's Theorum

  • Thread starter Titans86
  • Start date
  • #1
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Homework Statement



F = [−y^3, x^3], C the circle x^2 + y^2 = 25

Book gives answer as Pi*1875*1/2, I get Pi*1875

The Attempt at a Solution



[tex]\int\int(3x^2 + 3y^2)dxdy[/tex]

[tex]\int\int(75(cos^2\vartheta + sin^2\vartheta))rdrd\vartheta[/tex]

[tex]75\int[1/2 r^2]^{5}_{0}d\vartheta[/tex]

[tex]\frac{1875}{2}\intd\vartheta[/tex]

[tex][\frac{1875}{2}\vartheta]^{2\pi}_{0}[/tex]

[tex]=1875\pi[/tex] Where did I go wrong?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
When you have


[tex]
\int\int(3x^2 + 3y^2)dxdy
[/tex]

and then convert to polar coordinates x=rcos(theta) and y=rsin(theta)

r is not 5. r is a variable you are integrating.
 
  • #3
17
0
When you have


[tex]
\int\int(3x^2 + 3y^2)dxdy
[/tex]

and then convert to polar coordinates x=rcos(theta) and y=rsin(theta)

r is not 5. r is a variable you are integrating.
Of course!!! Thank you for the quick reply.
Regards,
Adam
 

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