Have a look at this

opinion piece from the mathguy on public radio.

Then think about this question I wrote in response.

Given the graph of $f(x)$ which of the following is the largest value?

$\begin{cases}a)~\int_0^6 {f(x)dx} &~b)\int_0^6 {f^2(x)dx} \\

c)~\int_0^6 {\sqrt{f(x)}dx} &d)~\int_2^6 {f^3(x)dx}\\e)~\text{cannot be determined}\end{cases}$

Over a period of years I gave this in a talk at to several meetings.

Meeting of secondary teachers of AP calculus & community college mathematics teachers.

In all of those sessions, I had only one correct answer.

I summit that this is exactly what Devlin was about in that link.

**No calculator, computer , or webpage would be of any help!**
Do you know the answer?

**Any one?**