The integral is split because is a piecewise-defined function. And that is so, in turn, because and are piecewise-defined functions. E.g.,
We have for all y. However, expanding leads to a piecewise definition. For example, for , but for .
I'm having trouble understanding the part of the solution that is between the asterisks.
************************************************** ************************************************** *************************
************************************************** ************************************************** *************************
I think my biggest question is, why is the integral split up instead of being over [2.7,3.3]?
The integral is split because is a piecewise-defined function. And that is so, in turn, because and are piecewise-defined functions. E.g.,
We have for all y. However, expanding leads to a piecewise definition. For example, for , but for .