₁^5(|x-3|+|1-x|) d x=

Step-by-step solution

₁^5[|x-3|+|1-x|] d x= ^5|x-3| d x+ ^5|1-x| d x= ₁^3|x-3| d x+ ₃^5|x-3| d x+ ₁^5|1-x| d x= ₁^3(3-x) d x+ ₃^5(x-3) d x+ ₁^5(x-1) d x= [3 x- x^2 2 ]₁^3+ [ x^2 2 -3 x ]₃^5+ [ x^2 2 -x ]₁^5= (3 3- 9 2 )- (3 1- 1 2 )+ ( 5 5 2 -3 5 )- ( 3 3 2 -3 3 )+ ( 5 5 2 -5 )- ( 1 2 -1 )= 9 2 - 5 2 - 5 2 + 9 2 + 15 2 + 1 2 = 9-5-5+9+15+1 2 = 24 2 =12