Show that `int_0^(npi+v)|sinx|dx=2n+1-cosv ,` where `n` is a positive integer and ,`0<=vltpi`

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

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

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

Prove that int_(0)^(infty)x^n e^(-x) dx=n!., 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

Evaluate int_(0)^(infty)(x^(n))/(n^(x)) dx, 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