This thread reminded me that there’s potential for a good number of nerdy jokes about how different professions would approximate an integral. For example:

Chemists:
Draw the curve on a piece of paper, precisely cut out the area, and mass it.

Experimental physicists:
Cut out the area and burn it in a highly accurate calorimeter.

Psychiatrists:
Medicate the paper until the curve is flat and then find the area of the rectangle.

Accountants:
Draw a separate, secret curve that causes everything to sum to zero.

Biologists:
What’s an integral?

Mathematicians:
What’s a number?
Okay, that’s all I got.

I’ve actually done this. The very old integrator attached to an HPLC in a lab at university failed, so we had to use an old pen chart recorder to obtain our peaks. To measure the concentration of whatever the heck the lab was for, my lab partner and I cut out the peaks and solved by mass ratio. IIRC we were accurate within about 10% of the expected value, which is impressive considering the paper was warped and yellowed from having been exposed to water and sunlight, and the pen line was about 4mm wide!

Astronomers: draw the curve and cut it out of the paper, and leave it standing still while the Earth orbits the Sun, and see if you can detect any shift in its appearance at repeated intervals 6 months apart. If that isn’t sensitive enough, compare the spectral absorption lines you see when looking at the near versus the far edge of it, for redshifting.