Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral `int_(0)^(5)[x]{x}dx` is -

Let {x} and [x] denote the fractional and integral parts of a real number x respectively. Solve 4{x}=x+[x] .

If [x] and {x} denote the integral part and the fractional part of a real number x ,then the number of negative real number (s) x for which 2[x]-2{x}=x, is

Let{x} and [x] denote the fractional and integral parts of a real number x respectively.Solve 4{x}=x+[x]

Let {x} and [x] denote the fractional and integral part of a real number x respectively. The value (s) of x satisfying 4{x} = x + [x] is/are

Let {x} and [x] denote the fractional and integral part of a real number x respectively. The value (s) of x satisfying 4{x} = x + [x] is/are

Let f(x) denote the fractional part of a real number x. Then the value of int_(0)^(sqrt3)f(x^(2))dx is

Let f(x) denote the fractional part of a real number x. Then the value of int_(0)^(sqrt(3))f(x^(2))dx is-

If [x] and {x} represent the integral and fractional parts of x respectively, then the value of sum_(r=1)^(2000)({x+r})/(2000) is

If [x] and {x} represetnt the integral and fractional parts of x , respectively, then the value of sum_(r=1)^(1000)({x+r})/(1000) is