Prove the following generalization of Eq. (1). Let C be
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Prove the following generalization of Eq. (1). Let C be a simple closed curve in the plane (Figure 8) S : ax + by + cz +
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Prove the following generalization of Eq. (1). Let C be a simple closed curve in the plane (Figure 8) S : ax + by + cz + d = 0 Then the area of the region R enclosed by C is equal to 1 2n C (bz ? cy) dx + (cx ? az) dy + (ay ? bx) dz where n = a, b, c is the normal to S, and C is oriented as the boundary of R (relative to the normal vector n). Hint: Apply Stokes
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