Greens Theorem clarification

Hi Doctor Taylor,

When using Green's Theorem, if we have the problem set up with the double integral of the partial of F2 - partial of F1. If the orientation is counter clockwise we leave the double integral positive, and if it is clockwise we make the double integral negative. Is that right?

Thank you,

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yes. specifically when the boundary curve ∂E is oriented counter clockwise and blah-blah-blah*



but when ∂E is oriented clockwise



*blah-blah-blah means E is a simply connected domain and its boundary ∂E is piecewise differentiable closed curve that doesn't intersect itself