1. Let w = (x-y) dx+(xy) dy Verify that * is a contravariant functor from finite

1. Let w = (x-y) dx+(xy) dy Verify that * is a contravariant functor from finitedimensional vector spaces to graded algebras.2. Use the Fundamental Theorem (Greens Theorem) to deduce the formula for thearea of an ellipse. Hint: find a 1-form whose exterior derivative is dx dy.