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_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

If [sin^(-1)x]^(2)+[sin^(-1)x]-2 le 0 (where, [.] represents the greatest integral part of x), then the maximum value of x is

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

If [sin^(-1)x]^(2)-2[sin^(-1)x]+1le0 (where, [.] represents the greatest integral part of x), then

int_-1^1 (x.sin^-1x)/(sqrt(1-x^2)) dx =2

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

The value of the integral int_(-2)^2 sin^2x/(-2[x/pi]+1/2)dx (where [x] denotes the greatest integer less then or equal to x) is

If I=int_-1^1 ([x^2]+log((2+x)/(2-x)))dx where denotes the greatest integer leq x , then I equals

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

If the value of definite integral int_1^a x*a^-[log_ a x]dx, where a >1 and [x] denotes the greatest integer, is, (e-1)/2 then the value of equal to