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)(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 t Then show that the integral int_(a)^(a+t)f(x)dx is independent of a .

If f(x) is an integrable function over every interval on the real line such that f(t+x)=f(x) for every x and real t, then int_(a)^(a+1) f(x)dx is equal to

If f(x) is integrable over [1,2] then int_(1)^(2)f(x)dx is equal to

If f is an integrable function, show that int_(-a)^a xf(x^2)dx=0

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

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then find the value of the definite integral int_(0)^(1)f(x)dx

The value of the integral int_(0)^(2a)[(f(x))/({f(x)+f(2a-x)})]dx is equal to a

Let f(x)=x-[x], for every real number x, where [x] is integral part of x .Then int_(-1)^(1)f(x)dx is

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

A periodic function with period 1 is integrable over any finite interval.Also,for two real numbers a,b and two unequal non-zero positive integers m and nint_(a)^(a+n)f(x)dx=int_(b)^(b+m)f(x) calculate the value of int_(m)^(n)f(x)dx