`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

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)^(2)[x-1]dx= Where [x] denotes the

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

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

int_(-1)^(1){x^(2)+x-3}dx, where {x} denotes thefractional part of x, is equal to

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

The value of int_(-2)^(1)[x[1+cos((pi x)/(2))]+1]dx where [.] denotes the greatest integer function,is 1 (b) 1/2 (c) 2 (d) none of these

The value of int_0^([x]) 2^x/2^([x])dx , where [x] denotes the greatest integer function is (A) [x]log2 (B) [x]/log2 (C) 1/2[x]/log2 (D) none of these

int_(0)^(9){sqrt(x)}dx, where {x} denotes the fractional part of x, is 5(b)6(c)4(d)3

int_0^pi sqrt((1+cos2x)/2)dx= (A) 0 (B) 1 (C) 2 (D) none of these