Evaluate ∫40(|x|+|x-2|+|x-4|)dx

Let I = ∫40(|x|+|x-2|+|x-4|)dx
0<x<4 ⇒ |x|=x
0<x<2 ⇒ |x-2|=-(x-2)
2<x<4 ⇒ |x-2|=x-2
0<x<4 ⇒ |x-4|=-(x-4)
I = ∫20 x + ∫20 2-x + ∫42 (x-2) + ∫40 4-x
= [x²/2]²₀ + [2x-x²/2]²₀ + [(x²-4x)/2]⁴₂ + [4x-x²/2]⁴₀
= 8 + (4-2) + (8-8) - (2-2) + 16 -8
= 8 + 2 + 0 + 0 + 16 - 8 = 20