Would the answer be 40, 10 ?
1 answer:
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When answering things like this do the brackets first, is there are parenthesis in the brackets do those but keep it in the brackets and work regularly after
Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle in the plane
, where the curl is
. Green's theorem applies here, so that
which means the value of the line integral is 3 times the area of the circle, or .
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.