_ 0.2 ^ 3.5 [x] d x= (where [x]= greatest integer not greater than x )

Step-by-step solution

aligned _ 0.2 ^ 3.5 [x] d x & = _ 0.2 ^1(0) d x+ ₁^2(1) d x+ ₂^3 2 ~d x+ ₃^ 3.5 3 ~d x & =0+[x]₁^2+2[x]₂^3+3[x]₃^ 3.5 & =0+(2-1)+2(3-2)+3(3.5-3) & =0+1+2+1.5 & =4.5 aligned