Hi there. I have the next exercice: Verify the Green theorem with the field , and the path which its image is the boundary positively oriented for the region between y

At first I've drawn this:

Then I've parametrized the path

Then I made the double integral:

In the last integral I've made the change of variables . As you can see I have a problem with a sign, in the 2. Perhaps I should take the opposite signs because lambda2 and lambda3 are "negative" oriented? I thought the sign should came naturally given by the parametrization, so I'm not sure what I did wrong here.

Bye and thanks