Question

What is the difference between using a double integral and a triple integral to find a volume?

Answer 1

if you want to find only volume, you use double integral of "height of object above from integration contour" and when using triple, you just integrate 1 over the whole object... Sorry I can't explain it well with language barriers...

Answer 2

ohhhh! So then whenever I use a triple integral to find a volume, the integrand is always one?

Answer 3

I think so...

Answer 4

@KingGeorge Is it so?

Answer 5

or @satellite73 ? Am I right?

Answer 6

You are correct. For a double integral you have to integrate some function, for a triple integral, you integrate 1.

Answer 7

I see. Thanks! But what does it mean, geometrically, if i have a triple integral with an integrand that is a function and not 1?

Answer 8

Geometrically, there are a few things you can be looking at. One, you're finding a 4-volume. That is, the 4-dimensional equivalent of volume.

Two, if the volume in the region you're integrating in has a changing density, you could be finding the total mass.