Question

Evaluate:

`int_-4^5 |x + 3|dx`

Answer 1

Let f(x) = |x + 3|

∴ f(x) = x + 3, if x + 3 ≥ 0, i.e. if x ≥ – 3

= –(x + 3), if x + 3 < 0, i.e. if x < – 3

∴ `int_-4^5 |x + 3|dx = int_-4^-3 -(x + 3)dx + int_-3^5 (x + 3)dx`

= `-[x^2/2 + 3x]_-4^-3 + [x^2/2 + 3x]_-3^5`

= `-[9/2 - 9] + [16/2 - 12] + [25/2 + 15] - [9/2 - 9]`

= `9/2 - 4 + 25/2 - 9/2 + 24`

= `20 + 25/2`

= `65/2`