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int(0)^(a) |x-1|dx...

`int_(0)^(a) |x-1|dx`

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`" Let I "= int_(0)^(4) |x-1|dx`
`:. I= int_(0)^(1) |x-1|dx+int _(1)^(4) |x-1|dx`
`=int_(0)^(1) (1-x)dx+ int_(1)^(4) (x-1) dx`
`=[x-(x^(2))/(2)]_(0)^(1) +[(x^(2))/(2)-x]_(1)^(4)`
`=(1-(1)/(2))-0+((4^(2))/(2)-x)-((1)/(2)-1)`
`=(1)/(2)+4+(1)/(2)=5`
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