[.] represents a greatest integer function.If _ 3 ^ 18 [x] d x=a+b 2 +c 3 , then a + b + c =

Step-by-step solution

_ 3 ^ 18 [x] d x= _ 3 ^ 4 [x] d x+ ₂^3[x] d x+ ₃^4[x] d x+ ₄^ 18 [x] d x= _ 3 ^ 4 1 d x+ ₂^3 2 d x+ ₃^4 3 d x+ ₄^ 18 4 d x=(2- 3 )+(2)+(3)+4( 18 -4)=2- 3 +2+3+4 18 -16=-9- 3 +12 2 aligned & =12 2 - 3 -9 & =b 2 +c 3 +9 aligned Where a=-9, b=12, c=-1a+b+c=2