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Question
Evaluate the following integrals using properties of integration:
`int_0^1 |5x - 3| "d"x`
Solution
f(x) = |5x – 3| = `{{:(-(5x - 3), "if" x < 3/5),(5x - 3, "if" x ≥ 3/5):}`
I = `int_0^1 |5x - 3| "d"x`
= `int_0^1 (3 - 5x) "d"x + int_(3/5)^1 (5x - 3) "d"x`
= `[3x - (5x^2)/2]_0^(3/5) + ](5x^2)/2 - 3x]_(3/5)^1`
= `9/5 - 9/10 + 5/2 - 3 - 9/10 + 9/5`
= `18/5 - 18/10 + 5/2 - 3`
= `9/5 + 5/2 - 3`
= `(18 + 25 - 30)/10`
= `13/10`
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