Need help figuring out limits of double integral

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SUMMARY

The discussion focuses on applying Green's Theorem to evaluate the integral of the vector field (6y + x) dx + (y + 2x) dy over the curve defined by the circle (x - 2)² + (y - 3)² = 4. The user successfully identifies the y-limits of integration as 1 ≤ y ≤ 5 but struggles to determine the corresponding x-limits. The solution involves using the equation of the circle to express x in terms of y, facilitating the integration process.

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DWill
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Homework Statement


Apply Green's Theorem to evaluate this integral:

Integral of: (6y + x) dx + (y + 2x) dy
over the curve C, where C is: The circle (x - 2)^2 + (y - 3)^2 = 4


Homework Equations





The Attempt at a Solution


To use Green's Theorem for this I would need to figure out the x and y limits of integration. With order of integration dx dy, I can see that 1 <= y <= 5. However I can't seem to figure out what the x limits would be. I've done similar problems except with a simpler circle centered at origin, so I'm sure this can't be that much more complicated..I'm just not getting it for some reason. Any suggestions?
 
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Well you have the equation of the circle. Use that to find an expression for x.
 

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