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- Integrate f(x,y,z)=18xz over the region in the first octant (x,y,z > 0) above the parabolic cylinder z=y2 and below the paraboloid z=8-2x2-y2.The solid bounded by the surfaces S1: −2 (z - 2) = y2 S2: x = 5 - 2z S3: x = 0 S4: y = 0 S5: z = 0 Corresponds to: The graphics are in the attached imageSet up a double integral for the volume of the solid bounded by the surface S with equation z + 8x + 4y - 24 = 0 and the region, R in the xy-plane inside the parallelogram whose vertices are (-1,-2), (-1,0), (1,2), and (1,4).
- Find the equation of the solid generated by revolving the region bounded by y=e-x^2 and the lines x=0, x=1, y=0 about the y-axis.What is the solid of revolution obtained when you revolve the region bounded by the curves y=x−1, y=0, and x=3 about the x-axis?Find the centroid of the homogeneous lamina bounded by the graph whose borders are f(x) = 16 − x2 and the x-axis