Deck 12: Extension E: Multiple Integrals

Question 1

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.

Answer 1

Question 2

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

A) 15.07
B) 16.25
C) 24.91
D) 13.92
E) 19.63

Answer 2

19.63

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

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

Question 5

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

Question 6

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

Question 7

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.

Question 8

Sketch the solid whose volume is given by the iterated integral

Question 9

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

Question 10

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

Question 11

Calculate the iterated integral.

A)
B) 8
C)
D)
E) None of these