> When I was taking a statics course, the professor taught us how to 
> calculate the center of mass by taking the shape, splitting up into 
> triangles, calculating the center of mass of each (formula for triangles), 
> and taking the weighted average.
>
> He never once mentioned the generic integral formulation. I asked him why. 
> He said, "That's good stuff to know if you're going to grad 
> school/academia, but in the real world, you almost never have the actual 
> function to integrate."
>
> Which is mostly true.

I guess it depends exactly what you're doing in the real world, but in the 
situations where I've used calculus I've known exactly the function to 
integrate (eg force applied at an exact point during a test).  If I didn't 
know the exact function I wouldn't be able to ask a finite element solver to 
do it either!

> If your colleague can work it out quickly on paper, it shouldn't take long 
> to do it on a computer (Maple, Mathematica, etc).

Sure, but the point is you need to have a good knowledge of calculus to even 
ask Maple of Mathematica to do such things.  If you have never been taught 
calculus at university then good luck trying to solve the problem with a 
computer math tool like Mathematica!

> Just because it's computers doesn't mean it has to be a finite element  or 
> Monte Carlo calculation.

It does for people who don't know calculus.

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