Question

Let $f:R\to R,g:R\to R$ be continuous functions. Then the value of indtegral
$\underset{In\lambda }{\overset{InI/\lambda }{\int }}\frac{f\left(\frac{x^2}{4}\right)\left[f\left(x\right)-f\left(-x\right)\right]}{g\left(\frac{x^2}{4}\right)\left[g\left(x\right)+g\left(-x\right)\right]}dx$

• A. depend on $\lambda$
• B. a non-zero constant
• C. Zero
• D. None of these

Answer 1

The correct option is A depend on $\lambda$

Given

$\Rightarrow \underset{In\lambda }{\overset{InI/\lambda }{\int }}\frac{f\left(\frac{x^2}{4}\right)\left[f\left(x\right)-f\left(-x\right)\right]}{g\left(\frac{x^2}{4}\right)\left[g\left(x\right)+g\left(-x\right)\right]}dx$

$\Rightarrow$ As the upper and lower Limit of the

integral depend on $\lambda$

$\therefore$ After integral the whole function will

depend upon $\lambda .$