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6.25. Let w be the following 2-form on R3: W= (x2 + y2)dy 1 dz + (x2 - y2)dx 1 dz. Let V be the
6.25. Let w be the following 2-form on R3: W= (x2 + y2)dy 1 dz + (x2 - y2)dx 1 dz. Let V be the region of R3 bounded by the graph of y = V1 x2, the planes z = 0 and 2 = 2, and the xz-plane (see Figure 6.4). 1. Parameterize V using cylindrical coordinates. 2. Determine dw. z 21 y 2 Fig. 6.4. The region V of Problem 6.25. 3. Calculate [ dw. V 4. The sides of V are parameterized as follows: a) Bottom: 0B(r,0) = (r cos 0,r sin 0,0), where 0
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