Question

Evaluate:

`int_0^6 |x + 3|dx`

Answer 1

Let I = `int_0^6 |x + 3|dx`

As, 0 ≤ x ≤ 6

`\implies` – 3 ≤ x + 3 ≤ 9

x + 3 > 0

`\implies` |x + 3| = |x + 3|

∴ `int_0^6 |x + 3|dx = int_0^6 (x + 3)dx`

= `[x^2/2 + 3x]_0^6`

= `(6^2/2 + 3 xx 6) - 0`

= 18 + 18

= 36