Ma 242 003
Download
1 / 44

MA 242.003 - PowerPoint PPT Presentation


  • 143 Views
  • Uploaded on

MA 242.003 . Day 44 – March 14, 2013 Section 12.7: Triple Integrals. GOAL: To integrate a function f(x,y,z ) over a bounded 3-dimensional solid region in space. . Step 1: Subdivide the box into subboxes . Generalization to bounded regions (solids) E in 3-space:.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' MA 242.003 ' - binh


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Ma 242 003
MA 242.003

  • Day 44 – March 14, 2013

  • Section 12.7: Triple Integrals


GOAL: To integrate a function f(x,y,z) over a bounded 3-dimensional solid region in space.



Generalization to bounded regions (solids) E in 3-space:


Generalization to bounded regions (solids) E in 3-space:

1. To integrate f(x,y,z) over E we enclose E in a box B

2. Then define F(x,y,z) to agree with f(x,y,z) on E, but is 0 for points of B outside E.

3. Then Fubini’s theorem applies, and we define


Definition: A solid region E is said to be of type 1 if it lies between the graphs of two continuous functions of x and y, that is



When integrals one can show that

the formula

Specializes to


When integrals one can show that

the formula

Specializes to


(continuation of problem 11) integrals one can show that


Definition: integrals one can show thatA solid region E is said to be of type 2 if it lies between the graphs of two continuous functions of y and z, that is


Definition: integrals one can show thatA solid region E is said to be of type 2 if it lies between the graphs of two continuous functions of y and z, that is


(continuation of problem 17) integrals one can show that


Definition: integrals one can show thatA solid region E is said to be of type 3 if it lies between the graphs of two continuous functions of x and z, that is


Definition: integrals one can show thatA solid region E is said to be of type 3 if it lies between the graphs of two continuous functions of x and z, that is


(continuation of problem 18) integrals one can show that


An Application of Triple Integration integrals one can show that

The volume of the solid occupying the 3-dimensional region E is


An Application of Triple Integration integrals one can show that

The volume of the solid occupying the 3-dimensional region E is


An Application of Triple Integration integrals one can show that

The volume of the 3-dimensional region E is

The area of the region D is


(continuation of problem 20) integrals one can show that


#33 integrals one can show that


(continuation of problem 33) integrals one can show that


(continuation of problem 33) integrals one can show that


(see maple worksheet) integrals one can show that


(continuation of problem 38) integrals one can show that


(continuation of problem 43) integrals one can show that


(continuation of problem ) integrals one can show that


(continuation of problem ) integrals one can show that


ad