Consider the functions f(x)=x g(x) and g(x)= [ 1 x ] Where [ ] is the greatest integer function. What is _ 1 3 ^ 1 2 g(x) d x equal to?

Step-by-step solution

aligned & _ 1 / 3 ^ 1 / 2 ~g (x) d x & ~g ( x )= array lc 2, & if 1 3 x 1 2 3, & if x= 1 3 array . aligned As g(x) is a gretest integer function so value of g(x) in integral limit will be So _ 1 / 3 ^ 1 / 2 g(x) d x= _ 1 / 3 ^ 1 / 2 2 d x aligned & =2[x]_ 1 / 3 ^ 1 / 2 & =2 [ 1 2 - 1 3 ] & = 1 3 aligned