Answer:
D.
Step-by-step explanation:
In the attached file
Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle <em>C</em> (the intersection of the hemisphere with the plane <em>y</em> = 0) with equation
Parameterize this circle by
with .
The surface is oriented such that its normal vector points in the positive <em>y</em> direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.
Now compute the line integral of F along <em>C</em> :