Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = i + (x + yz)j + (xy − sqrt(z )k, c is the boundary of the part of the plane 7x + 6y + z = 1 in the first octant.

By Stokes' theorem, the line integral of over is equivalent to the surface integral of the curl of over , where is the part of the plane in the first octant, with having positive/upward orientation.

Parameterize by

with and .

Take the normal vector to to be

The curl of is

Then the line integral is equivalent to

a. 19,958,400

step-by-step explanation:

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