A derivative calculator seems a lot easier to build as it much more “rule” based and solutions are usually what you would expect them to be. But how on earth can integral calculators figure out absolutely brutal integrals like sqrt(tanx) is in less than 5 seconds?
In: 102
Make many small squares and you get pretty good estimate quickly.
0->1.5 sqrt(tan(x))
10 small squares: 1.5154
100 small squares: 1.6706
1000 small squares: 1.6875
10000 small squares: 1.6892
100000 small squares: 1.6894
Error rapidly decreases when number of squares increase and calculators are very good at performing rapid calculations.
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