Brain Teaser - Area enclosed by a parabola and a line

[CR Haeger]

Franz - thank you for your post and straightforward solutions. I posted this thread in part, to see how others approached this "simple" problem by hand or with the assistance of a calculator. What I found so far, is that relying heavily on the HP Prime (CAS) still takes some problem setup, managing variables and managing syntax. For current algebra/calculus students** I can see where CAS can be helpful but can also complicate things. I also relearned that the HP15C is a great machine, especially in the hands of capable users.

Gerson - that is an interesting problem extension. I wondered how variations on f(x)=x^2 might be handled.

Best,
Carl

**or an old student looking at this again after a few decades of rust.