If `int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx`, then (A) `kgt1` (B) `0ltklt1` (C) `k=1` (D) none of these

int_0^1 e^(2-3x)dx

int_0^1 x^2 e^(2x) dx

int_0^1 e^x dx

int_0^1 (x/(x+1))dx

int_0^1 x(1-x)^(5/2) dx

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

int_0^4 (2x-1) dx

If a=int_(1/2)^2 1/x cot^7(x-1/x)dx , then (A) a=0 (B) 0ltalt1 (C) agt0 (D) none of these

1/4 int_(-1)^0 (x+2)dx-1/4 int_-1^0 x^2 dx

If [x] denotes the integral part of x and a=int_(-1)^0 (sin^2x)/([x/pi]+1/2)dx, b=int_0^1 (sin^2x)/([x/pi]+1/2)d (x-[x]) , then (A) a=b (B) a=-b (C) a=2b (D) none of these