Show that `int_0^(npi+v)|sinx|dx=2n+1-cosv ,` where `n` is a positive integer and `,lt=v

Show that int_(0)^(n pi+v)|sin x|dx=2n+1-cos v, where n is a positive integer and ,0<=v

The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive integer)

The value of the integral int_(0)^(a//2) sin 2n x cot x dx, where n is a positive integer, is

Show that 9^(n+1)-8n-9 is divisible by 64, where n is a positive integer.

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

Consider the integral I_(m) = int_(0)^(pi) (sin2mx)/(sinx ) dx , where m is a positive integer. What is I_(1) equal to ?

Solve (x-1)^(n)=x^(n), where n is a positive integer.

Consider the integral I_(m) = int_(0)^(pi) (sin2mx)/(sinx ) dx , where m is a positive integer. What is I_(m) equal to ?

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.