Intermediate E&M. Just need a check. Should be easy

[maherelharake]

Homework Statement

We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box?

Homework Equations

The Attempt at a Solution

I have attached what I did. I asked this yesterday, and someone told me my answer was correct (at the time I had 3E-15 C). However, I think I did something wrong, and redid my problem. Please let me know which way is correct, if either.

 

[Mindscrape]

Your x-bounds are strange. Why did you reverse them?

 

[maherelharake]

The teacher told me to do this. I was confused on it as well, but he assured me it is supposed to be in that order.

 

[maherelharake]

I am going to sleep soon. If you can please help me (it's due tomorrow morning) I will look at your response when I wake up.

 

[Mindscrape]

Oh nvm, the integration is right now that I take a second look at it. I got confused by the x going on bottom, but since it is negative that is all good. It looks like what you did is just fine. I don't know what the other way you did was, but this should be right (though I didn't actually do the numbers).

 

[maherelharake]

The other way was that I kept the bounds in terms of m and converted to cm at the end. However I think my numbers got messed up in the conversion. I think this way has less chance for error.

 

[Mindscrape]

Yeah, hah, that's precisely why I didn't do the numbers was because you really ought to convert cm to m for the integrand limits to make sure you get it right. Not converting and having cm*m floating around can get tricky.