There was a friend asking me how to prove
Mathematica showed that its approximate value is 1.99546, so I think it isn't easy to solve it, can you provide me some ideas about this question?
You may write
We are left to approximate ∫60x−xdx by a numerical integration rule. The point is that the second derivative of f(x)=x−x is not bounded on (0,6], in fact not bounded near 0+.
So let's write
leading to the series
and we are done, since we may now use the trapezoidal rule to approximate ∫61x−xdx taking into account that |f″