The_Big_K
#-Link-Snipped-# : That's excellent. Even Ramanujan was awesome at mental calculations and I'm looking to read about this great mathematician. I tend to take out calculator too but now trying to give up on the habit. It's quite embarrassing when the shop-onwer does quicker calculations than you and smiles back 😨 .Yeah, I agree that it helps in exercising the brain muscles.
A rather humorous yet typically CEan way of handling real life integrals in engineering:
In chemical engineering definite integrals are a daily event. Any experiments done will end up in a funny shaped curve to be integrated. There will be no analytical expression, which negates the normal approach. Numerical methods, which using a mechanical calculator, were literally a pain in the forearm.
What we did was to use a 0.1 mg accuracy Mettler balance. We had some precision graph pads from Germany. We accurately weighed 100 sq.cm of this and converted to mg/sq.cm.
Then each set of data was graphed, the shape cut out and weighed accurately. Multiplying by the previously calibrated area to weight constant gave the value of the definite integral instantly.
The curious thing is that some of us engineers (at least the CE variety) used to spend enormous time and effort coming up with such zany notions and validate them to simplify some activity, which would have been totally unnecessary if conventional methods were followed from the beginning.
It wouldn't be fun then would it?