It's been a few years since I became done with my university studies so I don't recall all the details very well. Today, I got into a discussion with my boss, also engineer, regarding computation of an area of a circle (not really so, but that's the significant point).
We tried to set up a double integral as follows:
$A = \iint 1 dr df, r \in [0, R], f \in [0, 2 pi]$
but apparently all the math since a few centuries has been very wrong because we "discovered" that the area is:
$A = \iint dr df = R \int df = 2 \pi R, $
which, of course, is the circumference. :)
My questions are those.
- Should I not integrate the function 1 over the specified area?
- What did we assume wrongly?
- Can I have a hint on how to integrate myself to the correct expression?
(Also, since I realize that I may be jumped with a gazillion of accusation yelling "homework", I can assure that I'm not a student - I can be Googled, Linked-in etc.)