- #1
In order for Green's Theorem to be applicable, the problem must involve a closed, simple curve. If the curve is not closed or has self-intersections, then Green's Theorem cannot be used.
If the problem involves a closed, simple curve and Green's Theorem is still not applicable, then it may be because the curve does not satisfy the other conditions of Green's Theorem. These conditions include the curve being continuously differentiable and enclosing a simply connected region.
No, Green's Theorem can only be used for closed, simple curves. Any other type of curve, such as open or self-intersecting curves, will not work with Green's Theorem.
Yes, there are other theorems and methods that can be used to evaluate line integrals and double integrals. Some alternatives include the Fundamental Theorem of Calculus, the Divergence Theorem, and the Stoke's Theorem.
If Green's Theorem is not applicable, you can try using one of the alternative theorems or methods mentioned above. Additionally, you can also try to break the curve into smaller, simpler curves that do satisfy the conditions of Green's Theorem.
