{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# calc2 - Triple Integrals Integration of a function of three...

This preview shows pages 1–3. Sign up to view the full content.

Triple Integrals Integration of a function of three variables, w=f(x,y,z), over a three- dimensional region R in xyz-space is called a triple integral and is denoted Triple Integrals in Box-Like Regions Suppose that R is the box with a<=x<=b, c<=y<=d, and r<=z<=s. The triple integral is given by To compute the iterated integral on the left, one integrates with respect to z first, then y, then x. When one integrates with respect to one variable, all other variables are assumed to be constant . For a box-like region, the integral is independent of the order of integration, assuming f(x,y,z) is continuous. Hence, there are total of 6 ways to order the integrations. For example we can integrate with respect to x, then z, then y. In this case we have

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

View Full Document
Consider the following example: The inner integral is Integrating with respect to z, treating x and y as constants, we obtain Note that z has completely disappeared from the expression on the right. The middle integral is with respect to y and x is treated as a constant. We have Note that y has disappeared from the expression on the right. The outer integral
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern