" If "I_(n)=int_(0)^( pi/4)tan^(n)xdx," then show that "I_(n)+I_(n-2)=(1)/(n-1)

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, prove that I_(n)+I_(n-2)=(1)/(n+1)

If u_(n)=int_(0)^((pi)/(4))tan^(n)xdx , show that, u_(n)+u_(n-2)=(1)/(n-1)(ngt1) , hence find u_(5)

let I_(n)=int_(0)^((pi)/(4))tan^(n)xdx,n>1

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

Let I_(n)=int_(0)^(pi//4)tan^(n)xdx,n in N , Then

If I_(n)=int_(0)^(pi/2) sin^(x)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int_(0)^(pi/2) sin^(x)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, show that (1)/(I_(2)+I_(4)),(1)/(I_(3)+I_(5)),(1)/(I_(4)+I_(6)),(1)/(I_(5)+I_(7)),... form an A.P. Find the common difference of this progression.

I_n= int_0^(pi/4) tan^(n)xdx then I_3+I_5 is