On my calculus final exam, I gave two questions about a metal plate of uniform density. The plate was easy to describe: it’s boundary was the axis and the parabola . In the first question, I asked for (the moment about the axis and in the second question, I asked for the center of mass (they could use symmetry to deduce ). So to find , they needed to find the area (mass) and .
What astonished me is that a number of students missed the question “find ” completely but then went on to solve for correctly!
This says something about the intellectually immature mind, but I am not sure what is says.