Use Stokes' theorem to calculate the integral for the surface S and boundary aS, and the given vector field F. Verify this result by calculating the line integral directly. S= {(x, y, z) : x? + y? + z? = 64, z > 0} (oriented as a graph). as = {(x, y) : x + y = 64}, oriented counterclockwise, and the vector field F = 7xi + 7yj + 7zk. (Give an exact answer. Use symbolic notation and fractions where needed.) evaluated line integral:

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