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A solid is bounded on the top by the paraboloid $z=r^{2},$ on the bottom by the plane $z=0,$ and on the sides by the cylinder $r=1 .$ Find the center of mass and the moment of inertia about the $z$ -axis if the density is a. $\delta(r, \theta, z)=z$b. $\delta(r, \theta, z)=r$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:18

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

26:18

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

19:34

Variable density A solid i…

31:43

A solid is bounded below b…

06:59

07:18

Variable density $A$ solid…

22:21

04:21

Let E be the solid in the …

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