1 / 9

110 likes | 291 Vues

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 can be integrated over a flat region in 2-space We can create a Riemann sum for the region W

Télécharger la présentation
## Section 16.3 Triple Integrals

**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.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**A continuous function of 3 variable can be integrated over a**solid region, W, in 3-space just as a function of two variables can be integrated over a flat region in 2-space • We can create a Riemann sum for the region W • This involves breaking up the 3D space into small cubes • Then summing up the volume in each of these cubes**If**• then • In this case we have a rectangular shaped box region that we are integrating over**We can compute this with an iterated integral**• In this case we will have a triple integral • Notice that we have 6 orders of integration possible for the above iterated integral • Let’s take a look at some examples**Example**• Pg. 801, #3 from the text, Find the triple integral W is the rectangular box with corners at (0,0,0), (a,0,0), (0,b,0), and (0,0,c)**Example**• Pg. 801, #5 from the text, Sketch the region of integration • Let’s set up the limits of integration for #15 on pg 801**Triple Integrals can be used to calculate volume**• Pg. 801, #18 from the text • Find the volume of the region bounded by z = x + y, z = 10, and the planes x = 0, y = 0 • Similar to how we can use double integrals to calculate the area of a region, we can use triple integrals to calculate volume • We will set f(x,y,z) = 1**Example**• Calculate the volume of the figure bound by the following curves**Some notes on triple integrals**• Since triple integrals can be used to calculate volume, they can be used to calculate total mass (recall Mass = Volume * density) and center of mass • When setting up a triple integral, note that • The outside integral limits must be constants • The middle integral limits can involve only one variable • The inside integral limits can involve two integrals

More Related