Suppose that `f: R to R ` is a continuous periodic function and T is the period of it . Let a `in R` . Then prove that for any positive integer n ` int_(0)^(a+nT) f(x)dx=n int_(a)^(a+T) f(x) dx`

Let f(x) be a continuous periodic function with period T. Let I= int_(a)^(a+T) f(x)dx . Then

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

suppose for every integer n, int_n^(n+1)f(x)dx=n^2 then the value of int_(-2)^4 f(x)dx is

Property 12:int_(a)^(a+nT)f(x)dx=n int_(0)^(T)f(x)dx where T is period of f(x)

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

Let f: R to R , be a periodic function such that {f(x):x in N} is an infinite set then, the period of f(x) cannot be