Green’s theorem

Q: I’m using the Green’s Theorem portion of the Calculus Made Easy app. It does not ask for the pathway etc… How do I enter the attached problem ?

A: Here we go , enter as follows
M,N = [y-x , 2x-y]

Now lets think about the path for moment: it is an ellipse starting at 2,0 passing through 0,2 , -2,0 and 0,-2 and back to 2,0 correct?
Ellipse equations in rectangular coordinates are : x^2/a^2 + y^2/b^2 = 1 , here a=2 , b=1 .Solving for y^2 yields:
y^2= 1-1/4*x^2 . Solving for y yields y= – + SQRT(1-1/4*x^2) which are lower and upper y bounds , enter them as such
and x bounds are [-2,2] . So the path is defined using x and y as rectangular bounds.

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