26-Triple Integrals - Triple Integrals John E. Gilbert,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Triple Integrals John E. Gilbert, Heather Van Ligten, and Benni Goetz Once weve seen the pattern of how to go from integrals of functions of one variable to double integrals of functions of two variables, then studying triple integrals E f ( x, y, z ) dxdydz of functions f ( x, y, z ) of three variables is a natural step, and a very important one in applications. Now the domain of integration is a solid E in 3-space, and when f > the integral is interpreted as the volume of the solid in 4-space below the graph of f and above E . Examples show how to write the triple integral as a repeated integral: Example 1: express the triple integral I 1 = E f ( x, y, z ) dxdydz as a repeated integral when E is the solid shown to the right above the rectangle D = [ a, b ] [ c, d ] in the xy-plane and below the graph of z = 6- x . Think of D as the base of E and the graph of z = 6- x above D as the top of E . Now fix a point P = ( x, y ) in D , and let z go vertically along the red line from P up to the black dot at the top.up to the black dot at the top....
View Full Document

This note was uploaded on 02/13/2012 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas at Austin.

Page1 / 4

26-Triple Integrals - Triple Integrals John E. Gilbert,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online