Question

Evaluate the following integrals using properties of integration:

`int_0^1 |5x - 3|  "d"x`

Answer 1

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`