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 int e^(2x)sin x cos xdx=(u)/(8)e^(2x)+c then u

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

If v_n=int_0^1x^n tan^-1xdx , show that: (n+1)u_n+(n-1)u_(n-2)=pi/2-1/n

If u_(n)=int(log x)^(n)dx, then u_(n)+nu_(n-1) is equal to :

If U_(n)=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n), then prove that U_(n+1)=8U_(n)-4U_(n-1)

if n is a set of prime numbers then the value of 10 U n = 2 A 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