1.

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

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Solution :`" 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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