Solution of IDZ Ryabushko 13.3 - Option 7

Section: Chapter 13. Multiple Integrals
Topic: Applications of Multiple Integrals
Description: Calculation of mass, static moments, moments of inertia, coordinates of the center of mass of plane and spatial bodies using double and triple integrals. Calculation of surface areas.

Tasks:
1. Compute the mass of a non-homogeneous plate D bounded by the given lines, if the surface density at each of its points is μ = μ(x, y).
2. Compute the static moment of a homogeneous plate D bounded by the given lines with respect to the specified axis, using polar coordinates.
3. Compute the coordinates of the center of mass of a homogeneous body occupying the region V bounded by the specified surfaces.
4. Compute the moment of inertia with respect to the specified coordinate axis of a homogeneous body occupying the region V bounded by the given surfaces. Take the density of the body δ equal to 1.

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