STATEMENT 1: Let `m` be any integer. Then the value of `I_m=int_0^pi(sin2m x)/(sinx)dxi sz e rodot` STATEMENT 2 : `I_1=I_2=I_3==I_m`

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

The value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi

STATEMENT 1: The value of int_0^(2pi)cos^(99)x dxi s0 STATEMENT 2: int_0^(2a)f(x)dx=2int_0^af(x)dx ,iff(2a-x)=f(x)

The value of int_0^pi (sin(1+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

If (m_i,1/m_i),i=1,2,3,4 are concyclic points then the value of m_1m_2m_3m_4 is

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

Given I_m=int_1^e(logx)^mdx ,t h e np rov et h a t(I_m)/(1-m)+m I_(m-2)=e

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

Find the value of (I ) sin^(-1) ( sin ((2pi )/(3)) ) (ii ) sin^(-1) (sin ((5 pi )/(4)))

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