Evaluate the line integral ∮f•dr by evaluating the surface integral in stokes' theorem with an appropriate choice of s. assume that c has a counterclockwise orientation when viewed from above. f = x^2 - y^2, z^2 - x^2, y^2 - z^2.c is the boundary of the square |x| ≤ 16, |y| ≤ 16 in the plane z = 0.

The vector field

has curl

Stokes' theorem says the line integral of along is equal to the integral of the curl of over a surface with as its boundary. Parameterize by

with and . Take the normal vector to to be

Then the line integral reduces to

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step-by-step explanation:

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