If `[x]` denotes the integral part of `x`, find `int_0^x[t+1]^3dt`.

Show that: (int_0^[x] [x]dx)/(int_0^[x] {x}dx)=[x]-1 , where [x] denotes the integral part of x and {x}=x-[x] .

If [x] denotes the integral part of [x] , show that: int_0^((2n-1)pi) [sinx]dx=(1-n)pi,n in N

If [x] denotes the integral part of x and f(x)=min(x-[x],-x-[-x]) show that: int_-2^2f(x)dx=1

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

Show that: int_0^[x] (x-[x])dx=[x]/2 , where [x] denotes the integral part of x .

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .

Evaluate: int_-100^100 Sgn(x-[x])dx , where [x] denotes the integral part of x .

Discuss the continuity of the function f(x){(a^(2)[x]+{x}-1)/(2[x]+{x}),x!=0log_(e)a,x=0atx=0 denotes greatest integral part and {*} denotes fractional part function.