The domain of `f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c),` where `a >0,b^2-4a c=0,i s(w h e r e[dot]` represents greatest integer function).

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

f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot] represents the 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_0^(10pi)[tan^(-1)x]dx ,w h e r e[x] represents greatest integer function.

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

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function). (a) n (b) 1 (c) 1/n (d) none of these

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] 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).

Discuss the differentiability of f(x)=[x]+|1-x|, x in (-1,3),w h e r e[dot] represents greatest integer function.