Exam 12: Extension E: Multiple Integrals

Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.

Find the moment of inertia about the y-axis for a cube of constant density 3 and side length if one vertex is located at the origin and three edges lie along the coordinate axes.

Use a triple integral to find the volume of the solid bounded by and the planes and

Find the mass of the solid E,if E is the cube given by and the density function is

Sketch the solid whose volume is given by the iterated integral

Express the integral as an iterated integral of the form where E is the solid bounded by the surfaces

Express the volume of the wedge in the first octant that is cut from the cylinder by the planes and as an iterated integral with respect to z then to y then to x.

Calculate the iterated integral.

Evaluate the triple integral.Round your answer to one decimal place.

Evaluate the triple integral.Round your answer to one decimal place. lies under the plane and above the region in the -plane bounded by the curves ,and

Express the triple integral as an iterated integral in six different ways using different orders of integration where T is the solid bounded by the planes and