# Let's do some calculus! (23)

Calculus Level 3

$\large \displaystyle \int_{\ln \lambda}^{\ln \left( {1}/{\lambda} \right)} {\dfrac{f \left( \dfrac{x^{2}}{4} \right) \big( f(x) - f(-x) \big)}{g \left( \dfrac{x^{2}}{4} \right) \big( g(x) + g(-x) \big)}} \,dx$

Given that $$f(x)$$ and $$g(x)$$ are both continuous functions. Does the value of the above anti-derivative depend on the value of $$\lambda$$?

Notations: $$\ln(\cdot)$$ denotes the natural logarithm function.