Question: 1. Given the planar lamina in the first quadrant bounded by the graph: y = 1 -x, with an area density: o(x,y) = kx, a)

1. Given the planar lamina in the first quadrant bounded by

1. Given the planar lamina in the first quadrant bounded by the graph: y = 1 -x, with an area density: o(x,y) = kx, a) sketch the lamina, and b) find the mass, center of mass, and Iy of the lamina. 2. a) Sketch the region R in the xy-plane bounded by: r = sin0. b) Sketch the surface S: Z= VX + y 2 c) Find the surface area of the portion of the surface S above the region R. d) Use a double integral to find the volume of the solid between the surfaces: Z =1X 2 + and z=0 above the region R

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