Prove that `int_(-pi/2)^(2pi)[cot^(-1)x]dx `,where` [dot]` denotes the greatest integer function.

Evaluate: int_((pi)/(2))^(2 pi)[cot^(-1)]dx, where [.] denotes the greatest integer function

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

Evaluate -int_(3pi//2)^(pi//2)[2sinx]dx , when [.] denotes the greatest integer function.

Evaluate: int_(0)^((5 pi)/(12))[tan x]dx, where [.] denotes the greatest integer function.

int_(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, is equal to

Evaluate: int_(-5)^(5)x^(2)[x+(1)/(2)]dx (where [.] denotes the greatest integer function).