||x − 1| − |x − 2|| Solve for piece wise function

Question

Hi i have to find in the itegral of the above function but i dont know how to first change this to the piece wise function, help

Answer 1

This isn't too hard to puzzle out but it will help you to graph the 3 functions involved.

On (-∞,1] ∪ [2,∞) y = 1

On [1,3/2] y = -2x + 3

and

on [3/2,2] y = 2x-3

The integral will, therefore, need to be defined on the 4 intervals defined above.

For example on (-∞,1} the integral is x.

On [1,3/2] the integral is x²- 3x.

If you need to define the interval across the division points, you need to add the values for the integral.