The value of `a (> 0)` such that `int_0^a[tan^(- 1)sqrt(x)]dx=int_0^a[cot^(- 1)sqrt(x)]dx` where [] denotes the greatest integer function, is

The value of the constant a gt 0 such that int_(0)^(a) [tan^(-1)sqrt(x)]dx=int_(0)^(a) [cot^(-1)sqrt(x)]dx , where[.] denotes the greatest integer function, is

The value of the constant a gt 0 such that int_(0)^(a) [tan^(-1)sqrt(x)]dx=int_(0)^(a) [cot^(-1)sqrt(x)]dx , where[.] denotes the greatest integer function, is

int_(0)^(pi) [cot x] dx , where [*] denotes the greatest integer function, is equal to

int_0^(pi) [cot x] dx , when [cdot] denotes the greatest integer function, is equal to :

Prove that int_0^oo[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest integer function.

int_0^(sqrt(pi/2))[[x^2]+cosx]dx (where [.] denotes greatest integer function)