Triple integrals, changing the order of integration

[amalone]

Homework Statement

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

Homework Equations

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

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

 

[SammyS]

Homework Statement

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

Homework Equations

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

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

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

 

[amalone]

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

Thanks!

 

[SammyS]

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