If `I_n=int_0^(pi/2) x^n sinx dx`, then `[I_4+12I_2]` is equal to (A) `4pi` (B) `3(pi/2)^3` (C) `(pi/2)^2` (D) `4(pi/2)^3`

If I_(n)=int_(0)^(pi//2) x^(n) sin x dx , then I_(4)+12I_(2) is equal to\

If I_(n)=int_(0)^( pi/2)x^(n)sin xdx, then {I_(4)+12I_(2)} is equal to (i) 3 pi( ii) 3((pi)/(2))^(3)( iii) ((pi)/(2))^(2) (iv) 4((pi)/(2))^(3)

IF I_n=int_0^(pi//4) tan^n x dx then what is I_n+I_(n+2) equal to

I_n=int_0^(pi//4) tan^n x dx, then lim_(ntooo) n [I_n + I_(n+2)] is equal to (i)1/2 (ii)1 (iii)infty (iv) 0

I_(n)=int_(pi/4)^(pi/2)(cot^(n)x)dx , then :

int_0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 (d) pi

int_(-(3pi)/2)^(-pi/2) {(pi+x)^3+cos^2(x+3pi)}dx is equal to (A) pi/4-1 (B) pi^4/32 (C) pi^4/32+pi/2 (D) pi/2

If I=int_(-pi)^pi e^(sinx)/(e^(sinx)+e^(-sinx))dx , then I equals (A) pi/2 (B) 2pi (C) pi (D) pi/4

If I_n=int_0^(pi/4) tan^nx then lim_(nrarroo)n(I_n+I_(n-2)) equals (A) 1/2 (B) 1 (C) oo (D) 0

int_0^(pi/2)sin4xcotx dx is equal to -pi/2 (2) 0 (3) pi/2 (4) pi