Question

Question #c0b80

Answer 1

Split up the integral into three pieces. For each piece, break up the domain at 1,2 and 3, respectively!

Explanation:

`int_{-1}^4 |x-1| dx = int_-1^1 |x-1| dx + int_1^4 |x-1| dx`
`= int_-1^1 (1-x) dx + int_1^4 (x-1) dx`
`= (x-x^2/2)_-1^1 +(x^2/2-x)_1^4 = {(1-1^2/2)-(-1-(-1)^2/2)}+{(4^2/2-4)-(1^2/2-1) }`
`= {1/2-(-3/2)}+{4-(-1/2)} = 2+9/2=13/2`

The other two pieces of the integral can be worked out in the same way - breaking up the domain of integration at 2 and 3, respectively.