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

Let f(x)=(sin^(101)x)/([(x)/(pi)]+(1)/(2)) , where [x] denotes the integral part of x is

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

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

The value of int_(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int_(-1)^(1) cos^(-1)[x^(2)-(1)/(2)]dx , where [.] denotes the greatest integer function , is

int_(-1)^(1){x^(2)+x-3}dx, where {x} denotes thefractional part of x, is equal to

f(x)=sin^(-1)[x^(2)+(1)/(2)]+cos^(-1)[x^(2)-(1)/(2)] where [.1 denotes the greatest integer function.

int_(0)^(x)({x}-(1)/(2))dx=(1)/(2){x}^(2)-(1)/(2){x}, where denotes the fractional part of x.

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

int_(-1)^(1)(sin^(-1)[x+(3)/(4)])dx=(pi)/(k), then k is where [1] denotes GIF )