[Hitchhiker 42]

I redid the midpoint spreadsheet - now at t=9.96s with dt=0.01s, the error is only 0.96. I replaced the Am column with the Am = sqrt(3*x').

Now to search for a possible explanation...
I did find this http://www.physics.drexel.edu/~steve...rs/simple.html

My guess would be that for this function, which, on the interval being examined, is concave up always (x'' > 0), the Euler method uses a point from farther back than the midpoint method to determine the slope (beginning of the interval slope vs. mid-interval slope). As it's concave up, the Euler method lags behind the midpoint method in growth, and so grows slower than the actual function by more than the midpoint method.

Now to test a method where it uses the end of the interval's slope...