Let R and C be as in Greens theorem, r ' a unit tangent vector, and n the outer unit normal vector of C (Fig 240 in Example 4) Show that (1) may be written or where k is a unit vector perpendicular to the xy plane Verify (10) and (11) for F 7x, 3y and C the circle x 2 y 2 4 as well as for an exampl...

We obtain div F in 11 from 1 if we take F F 2 F 1 Taking n y x as in Example 4 we get ...

Let R and C be as in Greens theorem, r' a unit tangent vector, and n the

Question:

Let R and C be as in Green€™s theorem, r' a unit tangent vector, and n the outer unit normal vector of C (Fig. 240 in Example 4). Show that (1) may be written

R п

(10) div Fdx dy = F•n ds 'R' pu.a-

where k is a unit vector perpendicular to the xy-plane. Verify (10) and (11) for F = [7x, -3y] and C the circle x² + y² = 4 as well as for an example of your own choice.

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