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Question
Evaluate:
`int_0^6 |x + 3|dx`
Solution
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
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