Chapter 13: Q. 18 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the moment of inertia about the y-axis is
Short Answer
The moment of inertia about y- axis is
Chapter 13: Q. 18 (page 1038)
Show that when the density of the region is proportional to the distance from the -axis, the moment of inertia about the y-axis is
The moment of inertia about y- axis is
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In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 41 with the order dy dx dz.
Identify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.
Find the masses of the solids described in Exercises 53–56.
The solid bounded above by the paraboloid with equation and bounded below by the rectangle in the xy-plane if the density at each point is proportional to the square of the distance of the point from the origin.
Evaluate the triple integrals over the specified rectangular solid region.
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