Exercise 49

Let E be the solid in the first octant bounded by the cylinder \(x^2 + y^2 = 1\) and the planes \(y = z, x = 0,\) and \(z = 0\) with the density function \(\rho(x, y, z) = 1 + x + y + z\). Use a computer algebra system to find the exact values of the following quantities for E. (a) The mass (b) The center of mass (c) The moment of inertia about the z-axis