Green's theorem

[jlmac2001]

Problem:

Use Green's Theorem to evaluate the line integral:

(integral over C) (2x dy - 3y dx)

where C is a square with the vertices (0,2) (2,0) (-2,0) and (0, -2) and is transversed counterclockwise.

Answer:

will the double integral be -1 dydx? What will they go from? Will it be from -2 to 2 and 0 to 2

[matt grime]

Answer: write down Green's theorem. comare it to what you have in the problem, decide which terms are in correspondence, and then do what you need to. the area is a diamond, your notional limits would give you a square.

is the problem really that you're not sure about the limits in double integrals?

two ways round this. 1, apply a transform to rotate the area to get a square. 2, thnk about it like this - imagine drawing vertical rectangles to apporximate the area, ie do y first, y goes from the lower boundary to the top, write the lower and upper boundary as functions of x - you will need to do two cases here for x negative and positive - those are the limits for y. then think about the x direction, which is, if you like, how are these rectangles positioned - here they start at x=-2 and end at x=2, so those will be the x limits.

[LASmith]

I have the same problem with the limits, how is it that you are able to approximate it as two rectangles?
Also, if you use the limits 2 and -2 for the x, I am unable to work how how you would find the limits for the y.