`int_0^x(2^t)/(2^([t]))dt ,w h e r e[dot]` denotes the greatest integer function and `x in R^+` , is equal to

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

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] denotes 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_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_0^((5pi)/(12))[tanx]dx , where [dot] denotes the 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)^(1.5) x[x^2] dx , where [.] denotes the greatest integer function

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to -2 (b) -1 z e ro (d) none of these

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to a. 1 b. 2 c. 2^n d. 2^(2n)

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