If f(x)= cases [x] [x] , & [x] 0 0, & [x]=0 cases where [x] denotes the greatest integer less than or equal to x , then _ x 0 f(x) equals

Step-by-step solution

aligned & As, f(x)= cases [x] [x] , & [x] 0 0, & [x]=0 cases & f(x)= cases [x] [x] , & x R-[0,1) 0, & 0 x 1 cases & RHL at x=0 & _ x 0⁺ f(x)= _ x 0 [0+h] [0+h] =0 & LHL at x=0 & _ x 0⁻ f(x)= _ h 0 [0-h] [0-h] & = _ h 0 (-1) -1 = 1 aligned Since, RHL LHL Limit does not exist.