[Bored chemist]

It hardly matters what order you do it in
Take F
Differentiate it using curl
integrate it
That takes you back to something with the same units as F
Then integrate it again.
That gets you something in units of "integrated F"

On the other side of the equation, you integrate F
That gets you something in units of "integrated F"

I'm not qualified to say if they are the same thing (except to say- of course they are it's a mathematical theorem).
But they clearly have the same units.

You should stop preaching about this.

[jeffreyH]

The definition of madness is repeating the same thing over and over again and expecting a different result. No matter how many times you argue that everyone else is wrong it won't make you right. Just picking random topics and arguing against them doesn't make you smart. If you want to waste your time that way go right ahead. But  you may well soon be arguing with yourself.

[alright1234 (OP)]

The area integral has precedence, The result of an integral is a length, area or volume. I my opinion any other application is false since Eudoxus (b. 390 BC) discovered that the area of a circle is proportional to the radius squared, and, Archimedes (b. 212 BC) derived the area equation for a circle using pi which was the most advance mathematics of the time. Determine the exact area of an equation was monumental achievement that modern physicists are attempting to destroy.

[Colin2B]

The result of an integral is a length, area or volume. I my opinion any other application is false since Eudoxus (b. 390 BC) 

Sorry, but science and maths have moved on since then. Important you keep up to date and don’t post false information.

[Bored chemist]

Determine the exact area of an equation was monumental achievement that modern physicists are attempting to destroy.

Can you clarify how scientists, who use calculus  every day are undermining calculus?

I my opinion any other application is false

Get a better opinion.

[alancalverd]

The result of an integral is a length, area or volume.

Obviously not. The time integral of acceleration is velocity, as every driver knows. The time integral of replication rate is population. The triple spatial integral of obtuseness is a waste of space.