`I_1=int_0^(pi/2)ln(sinx)dx ,I_2=int_(-pi/4)^(pi/4)ln(sinx+cosx)dxdot` Then (a)`I_1=2I_2` (b) `I_2=2I_1` (c)`I_1=4I_2` (d) `I_2=4I_1`

Evaluate: int_(pi//4)^(pi//4)log(sinx+cosx)dx

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

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

I_1=int_0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I_2=int_0^(2pi)cos^6xdx ,I_3=int_(pi/2)^(pi/2) sin^3xdx ,I_4=int_0^1 1n(1/x-1)dxdotT h e n I_2=I_3=I_4=0,I_1!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_2=I_3=0,I_4!=0

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

Consider I_1=int_0^(pi/4)e^x^2dx ,I_2=int_0^(pi/4)e^x dx ,I_3=int_0^(pi/4)e^x^2cosxdx ,I_4=int_0^(pi/4)e^x^2sinxdxdot STATEMENT 1 : I_2> I_1> I_3> I_4 STATEMENT 2 : For x in (0,1),x > x^2a n dsinx >cosxdot

L e tI_1=int_(pi/6)^(pi/3)(sinx)/x dx ,I_2=int_(pi/6)^(pi/3)(("sin"(sinx))/(sinx))dx ,I_3=int_(pi/6)^(pi/3)(sin(tanx)/(tanx))dx Then arrange in the decreasing order in which values I_1,I_2,I_3 lie.

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.

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

The value of I=int_(0)^(pi)x(sin^(2)(sinx)+cos^(2)(cosx))dx is