Why double integral could calculate area and volume

[transgalactic]

why there are a case where double integral could calculate area
and in other case
it could calculate a volume.

an integral should do only one thing
not both??

for what characteristics it could used to calculate area,
for what its volume

 

[tiny-tim]

Hi transgalactic!

It depends what you're integrating.

(did you have something specific in mind?)

For example, with an irregular solid you'd probably need 3 integrals, but with say an irregular cylinder (like a cookie-cutter ), all the heights are the same, so you only use 2 integrals .

 

[Mark44]

A definite integral (single, double, are whatever) just represents a number. It's only when we give it context by attaching dimensions (e.g., feet, cm, lb) to the quantities involved does it represent area or volume or work or what-have-you.

A single integral could represent an area, volume, length, probability, or any number of other concepts, depending on what we have decided to use for units. It's similar for double integrals.

What makes you think that an integral is supposed to do only one thing?