If f(x) satisfies f(1) = f(4), then what is  equal to?

Given:

f(1) = f(4)

Concept Used:

(i) Integration or Anti Differentiation or Primitive: 

If f & F are function of x such that F' (x) = f(x) then the function F is called a Primitive or Antiderivative or Integral of f(x) w.r.t. x and is written symbolically as 

  or  , Where c = Constant of integration

(ii)  = f(b) - f(a) 

Here, f(a) is the lower limit value of the integral and f(b) is the upper limit value of the integral.

Calculation:

According to the question we have to find the value of 

⇒  =  (Integration is the 'inverse' of differentiation)

⇒  = f(4) - f(1)

⇒ f(4) - f(4) = 0

∴  equal to 0.