Sun K.

# Use Stokes' Theorem to evaluate the surface integral?

Use Stokes' Theorem to evaluate the surface integral where F=<zx^2, z(e^xy^2)-x, x*ln (y^2)> and where S is the portion of z=1-x^2-y^2 above the xy-plane with n upward.

x^2+y^2=1 r=1

x=cos t

y=sin t

z=0

dx=-sin t

dy=cos t

dz=0

integral of zx^2 dx+z(e^xy^2)-x dy+x*ln(y^2) dz from 0 to 2pi

This doesn't match the answer in the book. Can someone please correct me and show the work with steps?

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