If `I_1=int_0^pixf(sin^3x+cos^2x)dxa n d` `I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx ,t h e nr e l a t eI_1a n dI_2`

IfI_1=int_0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I_2=int_0^(pi/2)(sin^2x)/(1+sin^2x)dx I_3=int_0^(pi/2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx ,t h e n I_1=I_2> I_3 (b) I_3> I_1=I_2 I_1=I_2=I_3 (d) none of these

u=int_0^(pi/2)cos((2pi)/3sin^2x)dx and v=int_0^(pi/2) cos(pi/3 sinx) dx

Evaluate int_(0)^((pi)/(2))(3sin^3x+4cos^4x)dx .

int_(0)^(pi/2) (sin x dx)/(1+ cos^2 x ) is

IfI_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)d ,a n dI_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

For x in R and a continuous function f, let I_1=int_(s in^2t)^(1+cos^2t)xf{x(2-x)}dxa n dI_2= int_(sin^2t)^(1+cos^2)xf{x(2-x)}dxdotT h e n(I_1)/(I_2) is -1 (b) 1 (c) 2 (d) 3

Iflambda=int_0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)dtheta,t h e n I_1=-2I_2 (b) I_1=I_2 2I_1=I_2 (d) I_1=-I_2

Q. int_0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I