Evaluate: `int_0^oo[2e^(-x)]dx ,w h e r e[x]` represents greatest integer function.

Evaluate: int_0^(10pi)[tan^(-1)x]dx ,w h e r e[x] represents greatest integer function.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_0^(100)x-[x]dx where [dot] represents the greatest integer function).

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

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integer function.

Evaluate: int_0^1 e^(2-3x) dx

Evaluate the following limits using sandwich theorem: lim_(x->oo)([x])/x ,w h e r e[dot] represents greatest integer function.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate int_(0)^(1)e^(2-3x)dx