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If f(x)a n dg(x) are continuous function...

If `f(x)a n dg(x)` are continuous functions, then `int_(1nlambda)^(1n1/lambda)(f((x^2)/4)[f(x)-f(-x)])/(g((x^2)/4)[g(x)+g(-x)])dx` is
(a)dependent on `lambda` (b) a none-zero constant (c)zero (d) none of these

A

depenent on `lamda`

B

a non zero constant

C

zero

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`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)
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