It's definitely a tricky problem for a student. The reason that everyone likes it is that this is exactly the kind of problem you run into when you need to solve an integral in the real world.
Once a year at least I run into a math situation like this. Obviously in some professions it will be much more (or less) often.
Exponents, floor, ceiling, and absolute value are very frequently part of the problem.
The approach of graphing the function, breaking it into components, and seeing if any of them are periodic, are all important steps toward a solution (more so than the symbolic manipulation because that might either be a big mess or even unavailable).
Often you'll end up using numerical methods to approximate the solution, but if you can come up with a closed form solution that's much nicer.
> Often you'll end up using numerical methods to approximate the solution, but if you can come up with a closed form solution that's much nicer.
Also even with the example in the post , thinking about the problem at first and exploiting it's periodicity before naively integrating numerically over the entire limit affords much faster computation. Although might not be specific to this example , utilising such symmetries can sometimes turn even a numerically intractable problem or a problem that requires days / 100s of gigabytes into something one can do on their laptop in hours.
Once a year at least I run into a math situation like this. Obviously in some professions it will be much more (or less) often.
Exponents, floor, ceiling, and absolute value are very frequently part of the problem.
The approach of graphing the function, breaking it into components, and seeing if any of them are periodic, are all important steps toward a solution (more so than the symbolic manipulation because that might either be a big mess or even unavailable).
Often you'll end up using numerical methods to approximate the solution, but if you can come up with a closed form solution that's much nicer.