[" and the lines "y=1" and "y=4.],[" (iv) 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 the value of overset(a+t)underset(a)int 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+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

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 .

If int_[x]^(x+1) f(t)dt =[x] then th value of int_(-2)^4 f(x) dx is equal

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

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

Prove that the value of the integral, int_(0)^(2a)(f(x))/(f(x)+f(2a-x))dx is equal to a.

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.