If `f(x)` and `g(x)` are continuous functions, then `int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx` is

Options

A. depenent on `lamda`
B. a non zero constant
C. zero
D. none of these

Answer

C

Explanation

`I=int_(log lamda)^("log"1/(lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx`
`=int_(log lamda)^(-log lamda)((f(x^(2)//4)[f(x)-f(-x))])/(g(x^(2)//4)[g(x)+g(-x)])=0`
(As the integrand is odd function)