Let's do some calculus! (23)

Calculus Level 3

lnλln(1/λ)f(x24)(f(x)f(x))g(x24)(g(x)+g(x))dx\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)f(x) and g(x)g(x) are both continuous functions. Does the value of the above anti-derivative depend on the value of λ\lambda?

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


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