Need help figuring out limits of double integral

In summary, the problem asks for the application of Green's Theorem to evaluate the given integral over the curve C, which is a circle. The x and y limits of integration need to be determined, with y ranging from 1 to 5. However, the x limits are not clear and may require using the equation of the circle to find an expression for x. The asker is having trouble with this and is seeking suggestions.
  • #1
DWill
70
0

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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  • #2
Well you have the equation of the circle. Use that to find an expression for x.
 

FAQ: Need help figuring out limits of double integral

1. What is a double integral?

A double integral is a type of mathematical operation used to calculate the volume under a surface in a two-dimensional space. It is essentially the sum of infinitely many small rectangles that make up the entire surface.

2. How do I know when to use a double integral?

A double integral is typically used when calculating the volume of a three-dimensional shape or when finding the area of a region bounded by two curves.

3. What are the limits of a double integral?

The limits of a double integral represent the boundaries of the two-dimensional space that is being integrated over. They can be expressed as a range of values or as functions of one or both variables.

4. How do I find the limits of a double integral?

The limits of a double integral can be found by graphing the region and identifying the boundaries of the shape or by using known equations or inequalities to determine the limits.

5. What is the process for solving a double integral?

The process for solving a double integral involves setting up the integral with the correct limits and integrand, evaluating the integral, and simplifying the result. It may also involve using techniques such as change of variables or integration by parts.

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