Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What is _ -1 ^0 h(x) d x equal to?

Step-by-step solution

array ll Given, & f(x)=|x-1| ...(i) & g(x)=[x] ...(ii) and & h(x)=f(x) g(x) & h(x)=h(x)-1 [x] ...(iii) array aligned _ -1 ^0 h(x) d x & = _ -1 ^0 f(x) g(x) d x & = _ -1 ^0|x-1| [x] d x & = _ -1 ^0(1-x) (-1) d x & = ₁^2(x-1) d x= [ x^2 2 -x ]₁^2 & = [0- ( 1 2 +1 ) ]=- 3 2 aligned