13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find...

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13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid region

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Transcript of 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find...

Page 1: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

13.6 Triple Integrals and Applications

Use a triple integral to find volume of a solid region

Find the center of mass and moments of inertia of a solid region

Page 2: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 3: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 4: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 5: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

Skip, if no time

Page 6: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 7: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 8: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 9: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

Just set up integral. DO NOT SOLVE!

Page 10: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 11: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 12: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 13: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 14: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.
Page 15: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

Find the moment of inertia about the z-axis from the previous problem.

Page 16: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

Other uses of triple integrals that your book does not go into…

• Density in terms of electrostatics (charge densities

• Potential energy due to the gravitational attraction between two point masses

Page 17: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

PG. 986 #1-5 ODD, 13, 17, 21, 23, 31Homework


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