[U_(n)=int_(0)^( pi/2)(sin^(2)nx)/(sin^(2)x)dx],[U_(1),U_(2),U_(3),...." is equal to "]

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If U_(n)=int_(0)^( pi)(1-cos nx)/(1-cos x)dx, where n is positive integer or zero,then show that U_(n+2)+U_(n)=2U_(n+1). Hence,deduce that int_(0)^((pi)/(2))(sin^(2)n theta)/(sin^(2)theta)=(1)/(2)n pi

If U_(n) = int_0^(pi/4) tan^(n) x dx then u_(n)+u_(n-2) =

Let u=int_(0)^(pi//2)cos((2pi)/(3)sin^(2)x)dx and v=int_(0)^(pi//2)cos(pi/3sinx)dx , then the relation between u and v is a) 2u=v b) 2u=3v c) u=v d) u=2v

If U_(n)=2cos n theta, then U_(1)U_(n)-U_(n-1) is equal to -

If u_(n)=int_(0)^((pi)/(2))x^(n)sin xdx then u_(10)+90u_(8) is equal to

Let u=int_(0)^((pi)/(4))(cos^(2)x)/(1+sin2x)dx,v=int_(0)^((pi)/(8))(1)/((1+tan2x)^(2))dx then the value of (u)/(v) equals