Homework Help: Triple integrals, changing the order of integration

1. Jan 31, 2013

amalone

1. The problem statement, all variables and given/known data

Write out the triple integral for the volume of the solid shown in all six possible orders. Evaluate at least 2 of these integrals.

2. Relevant equations

I attached a picture of the figure. The front : x/2+z/5=1
right : y/4+z/5=1

3. The attempt at a solution

I really need help with the possible orders and not the actual integration.
I figured out two different orders but I'm not sure how to post them properly
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Attached Files:

• e843d440-16d8-4a95-a336-b1f0860a7a84.jpg
File size:
8.8 KB
Views:
317
2. Jan 31, 2013

SammyS

Staff Emeritus
Hello amalone. Welcome to PF !

You can simply describe the order in which you do the integrations, along with the limits of integration.

For example:
(From inner to outer)
Integrate over x from x = 0 to x = 1 - 2z/5 .

Integrate over y from y = 0 to y = 1 - 4z/5 .

Integrate over z from z = 0 to z = 5 .​

You could learn LaTeX and write:

$\displaystyle \int_{0}^{5} \int_{0}^{1 - 4z/5} \int_{0}^{1 - 2z/5\,} dx\,dy\,dz$

3. Jan 31, 2013

amalone

Thanks!

4. Jan 31, 2013

SammyS

Staff Emeritus
How about describing the orders of integration that you've found ?