If `[x]^(2)-[x]-2>0` then `x` lies between, where `[]` is greatest integer function

The area bounded by y=x^(2),y=[x+1], 0 le x le 2 and the y-axis is where [.] is greatest integer function.

The domain of the function f(x)=(1)/(sqrt([x]^(2)-[x]-20)) is (where, [.] represents the greatest integer function)

Let f(x) = [x]^(2) + [x+1] - 3 , where [.] denotes the greatest integer function. Then

The range of the function y=[x^2]-[x]^2 x in [0,2] (where [] denotes the greatest integer function), is

int_- 10^0 (|(2[x])/(3x-[x]|)/(2[x])/(3x-[x]))dx is equal to (where [*] denotes greatest integer function.) is equal to (where [*] denotes greatest integer function.)

The value of int_0^([x]) 2^x/(2^([x])) dx is equal to (where, [.] denotes the greatest integer function)

The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix) is discontinous is (where [.] denotes greatest integer function)

Discuss the continuity and differentiability for f(x) = [sin x] when x in [0, 2pi] , where [*] denotes the greatest integer function x.

If a in R and the equation (a-2) (x-[x])^(2) + 2(x-[x]) + a^(2) = 0 (where [x] denotes the greatest integer function) has no integral solution and has exactly one solution in (2, 3), then a lies in the interval

The domain of the function f(x)=1/(sqrt([x]^2-2[x]-8)) is, where [*] denotes greatest integer function