Let V be the region bounded by the paraboloid z = x2 + y2 and the disc z = 1 (Figure 2 left), and let S be the boundary
Posted: Thu Jul 14, 2022 4:46 pm
Let V be the region bounded by the paraboloid z = x2 + y2 andthe disc z = 1 (Figure 2 left), and let S be the boundary of theregion V. Use Gauss’s theorem to set up the integral over thevolume, where the vector field is given by,𝐕=𝑥2𝐢+𝑥𝑦𝐣+𝑧2𝐤 ,the radius of the disc is r = 1, and 0 ≤ θ ≤ 2π in cylindricalcoordinates. Figure 2 (right) shows a cross-section of theparaboloid. For full marks, the setup of the integral mustinclude:i. Divergence of 𝐕ii. Correct limits of integration using a vertical sliceiii. Appropriate differential volume