If `f(x+1)+f(x+7)=0, x in R `, then possible value of t for which `int_a^(a+t)f(x)dx` is independent of a,is

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AA x in R STATEMENT 1: The possible least value of t for which int_(a)^(a+t)f(x)dx is independent of a is 12. STATEMENT 2: f(x) is a periodic function.

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx in Rdot STATEMENT 1 : The possible least value of t for which int_a^(a+t)f(x)dx is independent of ai s12. STATEMENT 2 : f(x) is a periodic function.

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx in Rdot STATEMENT 1 : The possible least value of t for which int_a^(a+t)f(x)dx is independent of ai s12. STATEMENT 2 : f(x) is a periodic function.

Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx in Rdot STATEMENT 1 : The possible least value of t for which int_a^(a+t)f(x)dx is independent of ai s12. STATEMENT 2 : f(x) is a periodic function.

If f(x)=f(a+x) , then prove that the value of int_(a)^(a+t) f(x)dx is independent of a.

If f(x)=f(a+x) , then prove that, int_(a)^(a+t)f(x)dx is independent of a.

If f(x) is periodic function of period t show that int_(a)^(a+t)f(x)dx is independent of a.

If f(x)= f(a+x) then prove that the value of overset(a+t)underset(a)int f(x)dx is independent of a.

Given a function f(x) such that It is integrable over every interval on the real line,and f(t+x)=f(x), for every x and a real t Then show that the integral int_(a)^(a+t)f(x)dx is independent of a .

Given a function f(x) such that It is integrable over every interval on the real line, and f(t+x)=f(x), for every x and a real tdot Then show that the integral int_a^(a+t)f(x)dx is independent of adot