Let be the manifold in consisting of all points such that
and
Then $\partial M$ is the circle consisting of all points such that
and
The map , where given by
is local parametrization on that covers . Orient so that belongs to the orientation, and give the induced orientation.
a)What normal vector corresponds to the orientation of ?
b)Let be the form
Evaluate
directly.
c)Evaluate directly , by expressing it as an integral over the unit disk in the plane.
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Please, help with part b)!