Let f(x)= [ x x ]+ [ 2 x x ]+ + [ 10 x x ] (where [.] is the largest integer). then, find the value of _ x 0 f(x) .

Step-by-step solution

As we know, _ x 0 x x 1 but it is actually less than 1 . So, _ x 0 [ x x ]=0=1^2-1 Similarly, _ x 0 [2 2 x x ]= _ x 0 [4 2 x 2 x ]=3=2^2-1 Hence, _ x 0 [n n x x ]=n^2-1 Therefore, aligned & _ x 0 f(x)= (1^2-1 )+ (2^2-1 )+ + (10^2-(1) . & = (1^2+2^2+ +10^2 )-(1+1+ +1 times ) & = 10 11 21 6 -10 & =385-10=375 aligned