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I’m a little confused. Doing a double integral of vectors dx and dy gave an area (vector) dA and A.

Thinking back to calc 1, when we had FUNCTIONS (not vectors) they gave the area under a curve.

Does this mean doing a double integral for vectors (line integral) gives an area spanned by those two vectors in 2D or 3D space.

A double integral for regular functions, therefore two variables, gives the volume of that function in 3D space?

Am I getting this right?

I tried asking someone the first part (about vectors) and they said that’s not necessarily true and now I’m even more confused .

I’m doing calc 3 at the same time as electricity and magnetism so I don’t know too much, our physics prof is teaching us what he thinks we need to know for our lessons.