`int_0^(2pi) e^(sin^2nx) tannxdx=` (A) `1` (B) `pi` (C) `2pi` (D) `0`

I=int_0^(2pi) e^(sin^2x+sinx+1)dx then

int_0^pi (sin((n+1)/2)x)/sinxdx= (A) 0 (B) pi/2 (C) pi (D) none of these

int_0^(pi/2) e^-xcosxdx

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

Period of sin^2 theta is(A) pi^2 (B) pi (C) 2pi (D) pi/2

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

int_0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

int_-pi^(3pi) cot^-1(cotx)dx= (A) pi^2 (B) 2pi^2 (C) 3pi^2 (D) none of these

int_-(pi/3)^(pi/3) (x^3cosx)/sin^2xdx= (A) 0 (B) 1 (C) -1 (D) none of these

If n=2m+1,m in N uu {0}, then int_0^(pi/2)(sin nx)/(sin x) dx is equal to (i) pi (ii) pi/2 (iii) pi/4 (iv) none of these