`int_(0)^(1)[x]dx=...`(where [x] denotes the integral part of x)

int_(0)^(2)[x-1]dx= Where [x] denotes the

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

Show that: (int_0^[x] [x]dx)/(int_0^[x] {x}dx)=[x]-1 , where [x] denotes the integral part of x and {x}=x-[x] .

Show that: int_0^[x] (x-[x])dx=[x]/2 , where [x] denotes the integral part of x .

Evaluate: int_-100^100 Sgn(x-[x])dx , where [x] denotes the integral part of x .

If int_-1^1(sin^-1[x^2+1/2]+cos^-1[x^2-1/2])dx=kpi where [x] denotes the integral part of x , then the value of k is …

int_(0)^(oo)[cot^(-1)x]dx (where [.] denotes the

int_(0)^(10)[x^(2)]dx, where [.] denotes the greatest

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.