# definite_integral of max function [closed]

The following code returns `1/2`

, however it can be easily verified that
$$\int_0^1 \max(x,\ 1-x)\,{\rm d}x = \frac34.$$
What's wrong?

```
from sage.symbolic.integration.integral import definite_integral
var('x')
definite_integral(max(x,1-x),x,0,1)
```

use

`max_symbolic`

Thanks!

`max_symbolic`

does lead to the correct answer, but I worry that using`max`

silently produces an incorrect answer - should Sage give an error or a warning about the issue at least?This is a common pitfall. You could have tried to see what

`max(x,1-x)`

answers.This is weird - both

`max(x,1-x)`

and`min(x,1-x)`

return`x`

. At very least this breaks the identity $\max(x,1-x) + \min(x,1-x) = 1$.With symbolic arguments,

`max`

and`min`

return the first argument. Hence:However,