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    Computing areas and volumes using multiple integrals.

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    (1) Find the volume of the solid bounded by the paraboloid x2 + y2 = 2z, the plane
    z = 0 and the cylinder x2 + y2 = 9.
    (2) Find the volume of the region in the first octant bounded by x + 2y + 3z = 6.
    (3) Find the area of the solid that is bounded by the cylinders x2+z2 = r2 and y2+z2 =
    r2.
    (4) Find the volume enclosed by the surfaces z = 8 − x2 − y2 and z = x2 + 3y2.

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    Computing areas and volumes using multiple integrals is investigated. The solution is detailed and well presented.

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