Presentation is loading. Please wait.

Presentation is loading. Please wait.

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.

Published byNancy Rice Modified over 9 years ago

Similar presentations

Presentation on theme: "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."— Presentation transcript:

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 region

2

3

4

5 Skip, if no time

6

7

8

9 Just set up integral. DO NOT SOLVE!

10

11

12

13

14

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

16 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

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

Download ppt "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."

Similar presentations

Kinetic and Potential Energy

Kinetic and Potential Energy
R3-1 Physics I Review 3 Review Notes Exam 3. R3-2 Newton’s Law of Universal Gravitation.

R3-1 Physics I Review 3 Review Notes Exam 3. R3-2 Newton’s Law of Universal Gravitation.
Electric Fields The Electric Field Electric Fields Lines Field due to a Point Charge Field due to an Electric Dipole Field due to a Line of Charge Field.

Electric Fields The Electric Field Electric Fields Lines Field due to a Point Charge Field due to an Electric Dipole Field due to a Line of Charge Field.
Monday, November 3 Review for Exam III Chapters 6, 7, 8(springs only) 9.

Monday, November 3 Review for Exam III Chapters 6, 7, 8(springs only) 9.
ME 221Lecture 151 ME 221 Statics Lecture #15 Section 4.3.

ME 221Lecture 151 ME 221 Statics Lecture #15 Section 4.3.
22-1 Physics I Class 22 Electric Potential. 22-2 Work Integral in Multiple Dimensions (Review)

22-1 Physics I Class 22 Electric Potential Work Integral in Multiple Dimensions (Review)
2006 Fall MATH 100 Lecture 81 MATH 100 Lecture 18 Triple Integral, II; centroid Class Triple integral, centroids Integration in other orders.

2006 Fall MATH 100 Lecture 81 MATH 100 Lecture 18 Triple Integral, II; centroid Class Triple integral, centroids Integration in other orders.
Chapter 12-Multiple Integrals Calculus, 2ed, by Blank & Krantz, Copyright 2011 by John Wiley & Sons, Inc, All Rights Reserved.

Chapter 12-Multiple Integrals Calculus, 2ed, by Blank & Krantz, Copyright 2011 by John Wiley & Sons, Inc, All Rights Reserved.
Chapter 12 12.7 Similar Solids Two Solids with equal ratios of corresponding linear measurements Ratios Not Equal Not Similar Ratios equal Solids are.

Chapter Similar Solids Two Solids with equal ratios of corresponding linear measurements Ratios Not Equal Not Similar Ratios equal Solids are.
1 Class #8 Center of Mass demo Moment of Inertia Moment of Inertia by superposition method Energy and Conservative forces Force as gradient of potential.

1 Class #8 Center of Mass demo Moment of Inertia Moment of Inertia by superposition method Energy and Conservative forces Force as gradient of potential.
(a) (b) (c) (d). What is (1,2,3)  (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2)  (3,4) (c) (1,3,4,2) (d) (3,1)  (4,2)

(a) (b) (c) (d). What is (1,2,3)  (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2)  (3,4) (c) (1,3,4,2) (d) (3,1)  (4,2)
Multiple Integration 14 Copyright © Cengage Learning. All rights reserved.

Multiple Integration 14 Copyright © Cengage Learning. All rights reserved.
 Continue using a mat plan and its side and top views to represent a 3-D solid  Learn a new way to represent a 3-D object: net  Learn about a special.

 Continue using a mat plan and its side and top views to represent a 3-D solid  Learn a new way to represent a 3-D object: net  Learn about a special.
Center of Mass and Moments of Inertia

Center of Mass and Moments of Inertia
7.1 Scalars and vectors Scalar: a quantity specified by its magnitude, for example: temperature, time, mass, and density Chapter 7 Vector algebra Vector:

7.1 Scalars and vectors Scalar: a quantity specified by its magnitude, for example: temperature, time, mass, and density Chapter 7 Vector algebra Vector:
Triple Integral in Cylindrical Coordinates

Triple Integral in Cylindrical Coordinates
Magnetic field of a steady current Section 30. Previously supposed zero net current. Then Now let the net current j be non-zero. Then “Conduction” current.

Magnetic field of a steady current Section 30. Previously supposed zero net current. Then Now let the net current j be non-zero. Then “Conduction” current.
Section 16.7 Triple Integrals. TRIPLE INTEGRAL OVER A BOX Consider a function w = f (x, y, z) of three variables defined on the box B given by Divide.

Section 16.7 Triple Integrals. TRIPLE INTEGRAL OVER A BOX Consider a function w = f (x, y, z) of three variables defined on the box B given by Divide.
Section 16.3 Triple Integrals. A continuous function of 3 variable can be integrated over a solid region, W, in 3-space just as a function of two variables.

Section 16.3 Triple Integrals. A continuous function of 3 variable can be integrated over a solid region, W, in 3-space just as a function of two variables.
 Intro to the Atomic Theory Elements, Atoms, and Subatomic Particles Bill Nye - Atoms.

 Intro to the Atomic Theory Elements, Atoms, and Subatomic Particles Bill Nye - Atoms.

Similar presentations

Ads by Google